If particles snap to grid once you get down far enough, then there are a finite, though very large, number of ways you could configure atoms and stuff them into a limited amount of space. Which trivially implies that the maximum amount of intelligence you could fit into a finite amount of space is bounded.

And of course you could also update perfectly on every piece of evidence, simulate every possibility, etc.. in this hypothetical universe. This is the theoretical maximum bound on intelligence.

If our universe can be well approximated by a snap to grid universe, or really can be well approximated by any Turing machine at all, then your statements seem trivially true.