If the AI ever does reconnect to the Milky Way...

And if they wanted to really spook the horses they could have re-establishing contact with the Milky Way be the scene right before rolling the credits.

What does it matter?
The Milky Way Galaxy is just a 'husk' of the galaxy it was.
So many planets burned and charred either way.
Let the Andromeda colonist return; there is nothing for them here anyway.

Well, there's Grunt as well. Those two are the only two who can survive that timespan.
I wouldn't mind seeing him as an aged krogan leader.
I think there are many obstacles on the road of truly showing the connection between the two galaxies, the number one being the different types of choices affecting the galaxy. I think it might be happen if they decide to have a canon world save for MW, but it'll lead to a shitstorm from both people wanting their choices to be reflected and people that wanted the canon world save to be used for a fourt MW ME game.
I don't care much either way at this point, but it might be fun to see the reactions if they truly unified the two galaxies, regardless of the solution used.

Another point against it though, is that the initiative speech stinks of propaganda on many levels, and it's not clear yet if the situation of Andromeda was actually a surprise or not for the leaders of the project (especially if the hidden reason behind it was escaping the Reapers). We have to know more before even stating if the connection of the galaxies was a real goal or a fake one.

Grunt can live 600 years as well. And EDI. Not to mention with the synthesis ending one might argue there won't even be death anymore.

The briefings mention one of the goals of the initiative is establish a contact between the two galaxies. Some people speculate the Nexus final phase might be a relay connected to the Citadel. 
We don't know thought if the connection goal is truly something the Initiative plans to achieve or is something related to a propaganda to incentivate people to join the project (which the briefings made people think about). 

...then we are back to the exact problem MEA tries to escape. Why are people keep forgetting the actual reason for MEA's existence?

I figured that was a case of them keeping the door open storywise, so if all goes swimmingly and a game or two later they start thinking they'd like to reintroduce the old home country the seed of the idea is already planted.

That might be the reason behind it as well.

Briefings manage to contradict text descriptions on site. "Make no mistake, this is a one way trip" vs "establish permanent trade route". 

Not necessarily. Establishing a connection between the galaxies could be a long term goal that they are well aware will take hundreds of years. It's still a one way trip for the humans going now. 

Perhaps but I think it's also a possibility that they'er using it to tell stories until they can come with a plan to work around the endings you never know. But either way we'er in Andromeda now so we'll see what happens next.