If I hit you on the head with a baseball bat, and you go unconscious, are you then dead?
Assuming I never regain consciousness, for all intents and purposes, yes. If and when I awaken, I'm aware of a previous existence and I consider it continual.
When you wake up, are you the same person you were before?
This reminds me of one of my time travel thought exercises. If someone went back in time and changed something about my past, and those ripples changed my memory of the event, were my memories actually changed?
Every morning I wake up and believe I went to sleep the night before. As far as I can tell, I lived before this moment, and as far as I can tell I am the same person. My sense of "self" is based on that perception. I'm open to the theoretical possibility that when I sleep, my "perception file" so to speak is erased and replaced with a new set of memories that I percieve as being entirely consistant. An organic firmware flash from "God" if you will.
It's simply that, if this is the case, I can't percieve it or change it and it is largely irrelevant.
It's much like positing to an atheist "If there was an omnipotent, omniscient being that decreed "I am beyond human detection"" would that make you believe in God? Does it really matter if it's not affecting you? I don't beleive it does. While I like thinking about things like this, every morning I wake up with perceptions that make an image of "self" and as long as that is the case, that is "me".