I think you are asking whether consciousness might be a fundamentally different “thing” from physics and thus hard or impossible to simulate.

I think there is abundant evidence that the answer is ‘no’. The main reason is that consciousness doesn’t give you new physics, it follows the same rules and restrictions. It seems to be “part of” the standard natural universe, not something distinct.

Can you look at any arbitrary program and tell if it halts without running it indefinitely? If so, you should explain how and collect your Nobel. Telling everybody whether the Collatz conjecture is correct is a good warm up. If not, you can’t solve the halting program either. What does that have to do with consciousness though?

Having read “I Am a Strange Loop” I do not believe Hofstadter indicates that the existence of Gödel’s theorem precludes consciousness being realizable on a Turing machine. Rather if I recall correctly he points out that as a possible argument and then attempts to refute it.

On the other hand Penrose is a prominent believer that human’s ability to understand Gödel’s theorem indicates consciousness can’t be realized on a Turing machine but there’s far from universal agreement on that point.