"Would straightforwardly simulating the quantum wavefunction in sufficient detail automatically give rise to sentients experiencing outcomes in proportion to the Born probabilities, i.e., reproduce our current experience?"

I suspect I'm misunderstanding the question, because I notice that I'm not confused, and that's usually a bad sign when dealing with a question which is supposed to be complicated.

Is this not equivalent to asking "If one were to simulated our entire universe, would it be exactly like ours? Could we use it to predict the future (or at least the possible space of futures) in our own universe with complete accuracy?"

If so, the immediate answer that comes to mind is "yes...why not?"