You wouldn't even need quantum computer neurons. We can simulate quantum nature on normal circuits, albeit not very efficiently. But for the experiment this wouldn't matter. The only important thing would be that you can measure it, which in turn would allow you to replicate it in some non-human circuit. And if you fundamentally can't measure this aspect for some weird reason, you will once again reach the same conclusion as above.

You can simulate it, but you usually use PRNG to decide how your simulated wave function "collapses". So in the spirit of the original thought experiment, I felt it more adequate to replace the quantum part (if it even exists) by another actually quantum part. But indeed, using fake quantum shouldn't change a thing.