In combat situations, many aliens will be captured alive.
This is one hundred per cent wrong.
Aliens don't get captured - they fight to the death. It is only through special efforts at capturing them that the human forces get to study a live one. Of course, before the "gloves off" event, aliens can be captured alive, but scientists can't perform adequate research on them because of their POW rights. In terms of game effects, this means the alien research tree is not available prior to the event.
The point is that it would not sound as some excuse for allowing us to research aliens, but that it would feel like an improvement in a certain matter, thus making up a coherent storyline. It will not "become" legal at start, you will "make" it legal through certain efforts.
I don't understand what's incoherent about not being able to research live aliens until a certain event. An improvement in a certain matter through certain efforts, as you put it, is not equal to a more "coherent storyline". Sometimes, events just happen even if you don't act yourself.
I digress, though. Let's get back to your original idea, of a separate facility to study aliens in secret. This would then be a separate base with only an alien containment? People would want to base a squad of soldiers there too, since they have the base anyway. And if you have a fully functional base, well, then what's the difference with having the alien research tree right from the start? Maybe because it's a bit more expensive? That's too insignificant to be part of any sort of plot. Especially since, as I said, you will be doing it "legally" very soon after the start of the game anyway.