If the universe is not computable, and if the non-computable aspects are relevant to the functioning of the human brain, then our ability to build a brain simulation is strongly limited. A functioning synthetic brain would have to leverage the same relevant natural phenomenon as a real brain; a mathematical simulation running on a standard computer would not suffice.

I do think that I actually agree with your earlier point that once we have a functioning synthetic brain, we can ignore subjective experience itself and just focus on its functional implications for the entire system.