What does that even mean to you?

The brain is a quantum device in that it's full of stuff and all stuff is somewhat "quantum".

Are you asking whether quantum mechanics is required for the human brain? We don't really have any way to know right now. We just don't understand the brain well enough to make any sort of conclusion about that.

My bet is that consciousness will be computable, mostly because I expect it will be radically less "magical" than everyone wanted it to be: I believe that we are mostly a story we tell ourselves and most of your lived experience is basically a "Simulate other hairless apes" network that got too big for its britches. I think we will quantify the portion of the brain that does the actual work of "Consciousness" and it will be a sadly small portion.

I think that means consciousness could be classical, but that doesn't preclude a consciousness that is dependent on some quantum phenomenon from also existing.