calculations coarse enough that they don't actually simulate a brain, yet specific enough to make some very good predictions about what a brain would do

Maybe, but when you're making mathematical arguments, there is a qualitative difference between a deterministically accurate prediction and a merely "very good" one. In particular, for any such shortcut calculation, there is a way to build a mind such that the shortcut calculation will always give the wrong answer.

If you're writing a thought experiment that starts with "suppose... Omega appears," you're doing that because you're making an argument that relies on deterministically accurate prediction. If you find yourself having to say "never simulated as a conscious being" in the same thought experiment, then the argument has failed. If there's an alternative argument that works with merely "very good" predictions, then by all means make it - after deleting the part about Omega.