For myself at least, consciousness is the product of the body and in particular the brain. Without any kind of high bandwidth connection between two bodies, I don't see how your proposal could work.

That said, I wonder if that offers a possible way to 'transfer consciousness' between a human and their robot copy - link both brains together and then once synchronised (whatever that means), shutdown the biological half. Like a sort of extended Ship of Theseus idea.

That's an interesting idea. I think as long as the continuity of consciousness happens then it doesn't matter and you would negate the copy problem.