I actually completed what I felt was my first pretty solid game last night; 5/6 AI on a smaller map, so not too challenging, but it felt like I made all the right moves. Except, of course, when I threw my 2000+ ship fleet into the first homeworld without realizing it had an eye. I had sacrificed so much just to get there that I said the hell with it, and went ahead and took out all nine posts and command just before being cut to shreds. Surprising and satisfying.
Anyway, I mention it because after that I saw the effect of the AIP jump virtually immediately; there was one semi-neutered system that I'd had most of the game (AI's com center still there), with a small garrison and turrets to keep it in check. Within minutes of the first AI falling, I saw my forces in that system begin to lose control.
So I booked it to the SuperTerminal, took it down back to where it was supposed to be, and had actually had a much easier time of the second guy than the first.
Related question to the topic: is it significantly advantageous to take out the harder AI first, if there are two different difficulties you're playing against? Sounds like the only real difference is that the weaker AI's homeworld will be being reinforced at a slower rate, thus slightly favoring leaving him for second.