Yes, it's an assumption to say consciousness is non-computable. But it's also an assumption to say it is computable. Not really a phenomenon we understand.

I agree that fleshy brains are probably not the only things capable of producing consciousness. I think it's actually fairly likely that a machine could be made that reproduces it, I'm just... really skeptical that it's gonna look anything like a Turing machine. It would certainly be convenient if it did.

As to brains being made of discrete units... there's some evidence to suggest it might not be. When you put a person (or any living thing) under general anesthetics, the thing the anesthetics target is microtubules within cells. And microtubules themselves have quantum mechanical properties. They've been shown to er, "do", super-luminescence in lab experiments (I don't understand quantum).

Admittedly, that's a lot of correlation and almost no direct example of causation. But it does suggest there's... something... there that needs more examination and research.