If I get to keep the qualia yes absolutely.
Sorry, I added the example of the SF story while you were replying to my post. In that story now there's two of the same person walking about, both of whom think they are 'him'.
The really disturbing this is, this might be what our lives are actually like. After all, our brains frequently stop being conscious and then summon consciousness back into being. Is it really the same consciousness though? Or is it a fresh newly synthesised process that just has memories from the last time your were conscious?
I still wouldn't use the teleporter though.
And to push it further, in what sense is each moment's consciousness the same as the previous?
But if consciousness is based on what is percieved from physical world, then the consciousness can really take different forms, be parallel, be one single consciousness, and even not be dependant on time at all.
I think more interesting concept, than comparing death with being partially unconscious, is losing your complete memory. If consciousness is related on having past memories and experiences, how can we say a person can be conscious and function without having any single recollection of anything that ever happened.