It does have bearing if your definition of consciousness rests on free will and you think that's incompatible with determinism. Now I don't think a lot of people seriously believe that [1] but it's not some logical nonsense.
[1] Off topic: I think most people are really compatibilist but a lot of them (like me) also believe in non determinism. Not believing in free will is really rare.
[1] Off topic: I think most people are really compatibilist but a lot of them (like me) also believe in non determinism. Not believing in free will is really rare.