The AI Progress can indeed be driven negative, however the actual benefit to you will be capped at a floor.
So, let's say you're at that 200 AIP at the moment, and you manage to reduce it by a mammoth 400 AIP via the superterminal. Your effective AIP might only drop to 100, maybe not even that low, but that's okay -- if you hover over the AIP indicator, you can see your full 400 in reduction is still "on the books." Next time you do something that causes your AIP to increase, it won't unless that increase also causes the floor to go up. Since the floor goes up a lot more slowly, you might see an increase of 100 AIP (so from 100 back to 200) from your next 300-400 actual AIP increased.
So you start at 200 actual, reduce it by 400, go to 100 effective, increase by 300-400 actual, and come back up to maybe 200 effective. Or thereabouts, anyway; the details of the actual math aren't right (and very by difficulty level, etc, anyway), but it's in that ballpark. The bottom line is that it is NEVER a bad time to reduce AIP, even if you might not see the benefit from that reduction immediately.
The only question, with a superterminal, is if you'll be able to really withstand it's onslaught very long at the start of the game. Those can be incredibly brutal, and get more so the longer you hold them, so be sure to make sure and plan for something like 6X the amount of defenses you think you need.