Without metagaming, does it make sense to recruit Bull?

It means he wants you to think there's no danger, either because he needs you to succeed or because he wants to be ready to backstab you after you do, and calculates that giving up whatever lead time he has before you figure it out is worth coming off as trustworthy. It doesn't mean there is no danger, and two years later it turns out there is.

If by that you mean your character doesn't see a danger, fair enough. But that's not exactly what you said.

It's illogical unless he's afraid you'll kick him out when you find out. Which is exactly the rationale he gives when you ask why he's being upfront about it.

While there's some chance you won't let him in if you know he's a spy, there's an even better chance that you'll kick him out if you find out in any way other than him telling you up front. And that he does tell you doesn't mean there is no plan: merely that he thinks telling you he's a spy won't impact it... either because it's exactly what he says it is, or because he's already factored in that he's just made whatever his plan is harder in exchange for the increased protection from being summarily fired.

I have to ask, again: you seem to be phrasing this in absolute terms, so is this you thinking from your character's POV? Or is this you deciding that Bull isn't a threat on your own logic?

If this is your character talking, again, fair enough: your Inquisitor could be thinking along these lines, and that is the very point of this thread. I could even make sense of the rationale, although you're a bit more cavalier about the chance that someone might try something like this than I would be. In particular, I'd caution that thinking "nobody would do that because the spy wouldn't survive" isn't the best metric for making judgement. People sacrifice agents all the time, and the Qunari mindset that a human (or humanoid) being is simply a cell of a much larger organism doesn't make it any harder for the brass to pull.

If on the other hand this is your personal reading of the situation... well, I was going to put this in spoiler tags, but LadyofNemesis and I have both already alluded to it, so it turns out the Qunari do use him during their attempt at backstabbing the Inquisitor years after the Elder One dies. (Call that a long con.) Or they try to: whether or not he obeys the orders depends on whether or not you already deprogrammed him. And if he does manage to backstab the Inquisitor, it's because the Inquisitor calculated that letting an admitted spy into their organization was safe, probably for the same reason you cite.

No man. I'm just telling you my personal honest opinion: He poses no danger by telling you that he's a spy.

It's perfectly fine to distrust him, that's why the game is an RPG but I'm just telling you how I see things, and if we're realistically talking about spies, then no spy who is an actual danger would tell you that he is one. Why would he confess it then ? Wouldn't it be more practical to just use a better cover story if his goal was to infiltrate your organization and extract information by pretending to be a different person ?

I don't know if I agree that he was ever deprogrammed by the inquisitor. It's an interesting discussion but I lean on the side that he was already deprogrammed by the time he had arrived in Southern Thedas. The character is bare as bones 

I understand what you good folk are saying... but that is just soap opera level plotting

I don't think any spy would ever admit the truth because it automatically jeopardizes their position. I interpreted the whole thing as an impression of his character: he is a very conflicted individual who might have compromised morals and integrity, a notable lack of loyalty and perhaps violent tendencies... all of which shows in Bull throughout the story.

Well, Viddasala acts as though he is, doesn't she?

I suppose; worst to worst, you could justify it by sending Bull on suicide missions and keeping him away from anything important. That way you get the benefit of a merc' and if he dies well, there goes a Qun-Spy so not something to get all that broken up about.