Disagree. In this idea there is a nearly universal assumption of "uploading" the mind in question, and therefore the disposal of the original sheath. So on a purely pragmatic level, the continued existence of the extracted mind is a lot less easy to verify, being that it no longer has an autonomous physical body.
Anyway, you have to admit it would make good science fiction.
"Learning to be me" by Greg Egan is a short story that covers this very ground, it's good.
Altered Carbon also treats this subject in pretty good depth. A little more pulpy than I imagine Egan's writing to be, but still fun. Thanks for the pointer!
Oh really, might read that. I read Black Man and enjoyed it. (possibly called something else if you're in the US, by the same author as Altered Carbon)