The minute they went back in time they already changed the future, whether or not they actually change anything. This by itself creates an alternate reality where he is still born, so he can't disappear. He simply won't be born in the new universe.
Unless they're going with a "The future can't be changed" kind of deal, in which case the universe will find another way for him to be born. Which, I suppose, is what they wanted to see - moreso to make sure she can't do the same to them to make them disappear from this timeline.
Either way; I loved the finale. I hope they pick up a second season so it doesn't have to end like that ~.~I want to know! Personally, I don't believe Alec supports Kagami's plans; I think it's a "Greater good" kind of deal, where he needed him to go back in time with her to stop something.
Edit: I just thought of something - didn't Kagami say to Alec that "You told me about this moment where I spoke to you" or something like that? Which would hint that they are, indeed, the same universes?