Is there an "impossible" Inquisitor?

Atheist mage Adaar.

No, it is just the most unfitting combination for the Inquisitor and Herald of Andraste.

It is silly to talk about an impossible option. There is no such thing. If that's what you want, find a mod that allows you to play as a mage dwarf. Or, roleplay your way into a desirable narrative.

Just noticed this thread. Whilst I don't think there is any background that is impossible so far as the writers are concerned, I've always maintained that the Dalish Inquisitor is very improbable, particularly if they are a mage. Think about it. The Chantry have promoted a very negative view of the elves ever since the Exalted March on the Dales. Hence the extreme prejudice against city elves that sends that back to the alienage even when they have tried to make it outside (conversation in DAO). Now the Dalish aren't just any old elves. They have the marks of their religion literally on their faces, which would be immediately noticeable to anyone, so they can't just try to blend in and pass themselves off as elven servants. This is meant to be a highly sensitive and important Conclave to determine the future of the relationship between mages, Templars and the Chantry. So, security ought to have been very stringent. The human Inquisitors have a valid reason to be there, either through having been in a Circle or because of their family's close connection with the Chantry. The Vashoth Inquisitors are there as part of a mercenary band giving greater security to the proceedings, which could account for a mage Adaar getting a pass from Leliana/Cassandra or whoever else was in charge, even Justinia herself. The dwarf could have legitimate reason to get as pass because the Carta have arranged for supplies to the site or some such excuse. Lavellan has no such justification for their presence. I suppose they might be able to sneak in if they keep their hood up but I still say that makes for very lax security. However, Cory and his Grey Wardens also managed to gain admittance, so security is indeed very lax.  There is absolutely no reason Grey Wardens should have been there and every reason to be excluded bearing in mind that Anders was a Grey Warden deserter and Fiona a former Grey Warden who admitted leaving the Wardens and returning to the Circle specifically to cause trouble, both of whom were responsible for the mess being debated.  

I also never understood how the Keeper heard about the Conclave up in the Freemarches (gossip when trading with a human settlement I suppose) or why they thought they should send anyone to it, considering the Chantry and Templars had always been hostile to the Dalish mages, so it is unlikely the situation was likely to change through anything that was decided at the Conclave. If they had been based in Ferelden, I could just understand it as it wasn't too far to travel out of curiosity, but Lavellan would have to travel to the coast, get passage across the Waking Sea and then make their way to Haven as a solitary Dalish, who would always be in danger of attack along the way. It hardly seemed worth the risk.

So, whilst the writers didn't see fit to explain why this was possible, it does seem to me that a Dalish Inquisitor is as near as you will come to someone who should not have been there and whose presence should have been impossible.

I've been checking what it actually says about a mage Lavellan.
[Player name] manifested a talent for magic as a child. The clan's leader, Keeper Deshanna Istimaethoriel Lavellan, taught [him/her] how to control and hone [his/her] new powers. [Player name] grew into a capable mage, far away from the eyes of the templars and mage Circles. When tension between the two factions erupted into warfare, spilling into the countryside, Clan Lavellan was forced to pick up and move. [Player name]'s Keeper sent [him/her] to spy on the Conclave at Haven, as the outcome might determine the fate of [his/her] own clan.

It doesn't actually say you are the First to the Keeper, so we could infer that perhaps they were the "Spare", so the Keeper could afford to let them go.    I doubt this would have been the attitude of a DAO Keeper, where mages were regarded as precious to the clan and a sign they were recovering their ancient abilities, but it does make sense in light of the 3 mage rule retcon in DAI, where apparently mage children are just abandoned in the woods if the clan has too many of them.   Lavellan can deny their clan does anything so barbaric, which could be ironic if in fact that is exactly what the Keeper was doing but just didn't tell them as much.   So, essentially the Keeper has just discovered another child within the clan has come into their magic, which means they now have one too many, so the Keeper comes up with the bright idea of giving them an important mission outside the Freemarches, from which it is highly likely they will ever return.  (I'm such a cynic)

I also notice that it says we were alerted to the tension in the Chantry when the conflict spilled over into the countryside but that still doesn't explain how they heard about the Conclave, particularly as the clan moved specifically to get away from the fighting, so less likely to pick up news from beyond their immediate locality. It says the Keeper sent you because the outcome might determine the fate of the clan, which is still a puzzle to me because I don't see how the outcome would materially affect the clan either way, apart from the countryside returning to the state it was in prior to the civil war affecting it, which the clan would know about through observation and scouting in the Freemarches, not sending someone to spy on the council where the decision was made.

Incidentally, if it was so important to the Keeper to be kept appraised of developments, how was Lavellan supposed to say in touch? We had never previously seen the clans using long distance communication such as ravens and without this, if something was decided that was going to be an immediate threat to the clan, it would take Lavellan weeks to report back directly. (I have to admit this does fit with the idea that the Keeper never expected them to return if you are a mage but not a hunter/scout.   May be they were a trouble maker so it was a convenient way to get rid of them too).

As I've said, I feel this background was the least thought out when it came to justifying their presence at the Conclave. A city elf would have made more sense, attending as a servant, although that would have ruled out a mage, unless they did the same as for DAO and you were a city elf from a Circle. Presumably, though that would have changed the dynamics between them and Sera but particularly with Solas, so they opted to fudge an excuse and hope no one questioned it too deeply.

I'm pretty sure the dream bit does come up in game because when I saw that also happened to a Dalish in Tevinter Nights in The Dread Wolf Take You, I immediately recalled what had been said about our Keeper. (On did someone on these board suggested that may have happened?) So, if the "Dalish" in TN was legit and was responding to a dream, rather than this just being a story his group came up with to explain his knowledge, I had to assume the dream could only have come from Solas, since it was his followers who subsequently appeared on the scene. This being the case, could Solas have seen the Keeper through the Fade and sent the dream that prompted their spy to attend the Conclave? This seems a bit convoluted but it also seems a bit odd if they would have had the dream otherwise. So, possibly we are both remembering a theory on these boards rather than something in game.

I can confirm this was an option for conversation in game. I played three different Lavellans with different motivations and reasons that I devised for their backstory:

My first Lavellan was a female mage. She hadn't been born in the clan but in an alienage and then was smuggled out by her family to the clan when she came into her magic in order to keep her out of the Circle. Thus, as she had direct knowledge of human ways and some of the issues likely to be involved at the Conclave, it made sense the Keeper would send her and that she would want to go.

My second Lavellan was a male hunter/guardian. He had led the group responsible for protecting the clan. Since the Keeper thought spying on the Conclave might be important to the future safety of the clan, he volunteered to go. Since he was also gay, this accounted for why he had no family responsibilities to keep him there and why he argued it was better to send him than one of the other members of his team. He was highly capable of surviving by himself on the long journey.

My third Lavellan was the rebel apprentice mage. It wasn't that he didn't value Dalish culture but he did question some of the more illogical parts of it. He also argued they should have more interaction with humans in order to improve relations. Unsurprisingly, when the time came to select someone for the spy mission, he volunteered himself and the Keeper was only too happy to agree to his proposal. He was under no illusion why she was so ready to agree with him. Hence, I opted for the dialogue that said as much. I had a lot of fun playing this Lavellan. Rather than politely tell Cassandra that he had his own gods, he happily embraced his title of Herald of Andraste, pretending to be a believer. He decorated Skyhold with Chantry regalia, made all his decisions with reference to Andraste and generally milked the prophet angle for all he was worth, finding it both ironic and hilarious everyone seemed to buy into his bullshit.  I particularly enjoyed the praise he got from Vivienne.   Finally, he faced down Corypheus with the lines "And I'm the Maker's Chosen". Sadly, the only thing I couldn't bring myself to do was annoy Solas sufficiently that he got the hostile rather than admiring response from him. At the time, I didn't realise just how different the dialogue between them could be if you chose the hostile path but, to be honest, you do have to make some pretty questionable decisions to qualify and I find it hard to play absolute jerks. My rebel Lavellan was still essentially a good guy, just an irreverent one.   May be Solas did see through his act but appreciated his style and found it amusing, hence the approval.

I'm not sure if you can express a belief that you are the Herald of Andraste at the same time as professing belief in the elven gods, certainly in the conversation with Cassandra I recall it is an either one or the other situation. I think that related more to your belief in the Maker though from what I recall. If, instead of saying you do, but instead state you have your own gods, Cassandra responds with the suggestion that can't you find room for one more. I always found this odd because it was a fundamental dogma of the Chant of Light that there is only one god, the Maker, and all other gods are false, so I can only assume Cassandra was being extremely tactful for some reason in suggesting the Maker could be just one of many in your elven belief system.

However, it is possible you can start off stating your belief in your own gods but then affirm your belief in the idea you are the Herald of Andraste when talking with Giselle in the refugee camp after fleeing Haven, as I'm pretty sure it is still an option there. Not having done both, I don't know how this works out with regard to dialogue options further down the line.