I think you misinterpreted my comment. The poster I was responding to was talking about how it would not be the same consciousness, but a clone of that consciousness.

I am not making any unprovable claims about a spirit/soul, though I do not completely shut out the possibility there is something we haven't measured yet. I believe that externally, there is no difference in your scenario.

I think where there might be a difference, is to the consciousness itself. The continuity of that experience being the difference. In which case, gradually replacing the brain should be a solution to the continuity problem (like the Ship of Theseus). Where I think this is conceptually weakest, is when considering how much continuity of consciousness exists while sleeping or being sedated.