QM is a testable hypothesis, so I don't think it's necessarily like an axiomatic assumption here. I'm not sure what you mean by "it tells us nothing, as ... can't be built". It tells us there's no theoretical constraint and only an engineering constraint to doing simulating the human brain (and all the tasks)

Sure, you can simulate a brain. If and when the simulation starts to talk you can even claim you understand how to build human intelligence in a limited sense. You don't know if it's a complete model of the organism until you understand the organism. Maybe you made a p zombie. Maybe it's conscious but lacks one very particular faculty that human beings have by way of some subtle phenomena you don't know about.

There is no way to distinguish between a faithfully reimplemented human being and a partial hackjob that happens to line up with your blind spots without ontological omniscience. Failing that, you just get to choose what you think is important and hope it's everything relevant to behaviors you care about.