Theoretically the Infinity Brain can do... anything. Or rather, there is nothing in this realm that it could not do. Or rather... huh.
Well, it's as if you are writing a story, right? And in that story you can have anything happen that you want! But perhaps some things wouldn't make sense, so it does somewhat have to follow the "rules" in that story. But since you are writing the story you can make the rules change as you need to, mostly.
The Infinity Brain is almost like tricking the universe into believing that it is the "writer" for all reality. However, as it does not actually have any ability to think or act, nothing happens, even when it is perfected.
But if someone was to use it, to nudge it towards actions... then they could make ANYTHING happen. If they can believe that it can happen.
POSSIBLY the universe rejects it completely, and then it, and anything in an unknown radius around it would instantly collapse into some kind of hyper dense impossibly small point, and then everything around THAT would get dragged in, and so on.
BUT WELL WORTH THE RISK!!
-Notes on the Infinity Brain by Kay. Accompanied by frenzied scribbles.