It does if it changes the implications of being "dead". Death is only important if it's permanent.
I admit that reversibility would change the significance of death quite a bit, but that's still different from its existence. But while the person in question is atomized, before they are re-assembled, how are they NOT dead? Because there's no reason they need to be re-assembled, and if they never are, aren't they really and truly dead? A classification of current state which depends on future state isn't one I think we want to use, which would therefore mean that they're dead even if we end up resurrecting them or creating an exact copy.
By that definition, any procedure or occurrence that changes your body in any way makes you a different person.
In a sense, yes (and even without this interpretation, it's hard to deny that something fundamental has changed about your identity since you were a baby), but there's a continuity to an ordinary, non-teleported life (meaning that change was continuous and without interuption, providing a single thread we can label and follow despite the changes) that would disappear in our hypothetical imperfect-reproduction scenario. The thread breaks upon reproduction, and never restarts from exactly the same spot it stopped.
This is getting into philosophy, but my belief is that a "person" is simply the sum of his experiences and memories. Providing those survive the process, then the person that comes out is the same as the one that went in.
Yes indeed, these are largely philosophical discussion, and to a certain extent you can just adopt a definition for terms and be done with it. The point of these discussions, as I see it, is more to think about what such different definitions would mean in different situations - they sometimes produce results which are unsatisfying, and hence challenge us to search for new definitions which might be more satisfying.
For example, what happens if we take a scan of you to measure everything about you, store it in a computer, then recreate a copy of you as you were when you were scanned. Who is the person of tsg? What if we scan you again a day later, and create yet another version of you. Is that too tsg? Does it matter if we create more than one copy simultaneously, so they start out identical together? Certainly all three of these bodies are not equivalent anymore, so who is the person? Do they really have anything resembling the constant identity you seemed to object that I was throwing out? What happens if we kill the original body after making the copies - have we killed the person of tsg? I'm not saying your definition is wrong - as a definition alone it can't be - just putting forward some questions to probe the consequences of that definition.