Consciousness is often said to disappear in deep, dreamless sleep. We argue that this assumption is oversimplified. Unless dreamless sleep is defined as unconscious from the outset there are good empirical and theoretical reasons for saying that a range of different types of sleep experience, some of which are distinct from dreaming, can occur in all stages of sleep.
I would argue that two disconnected copies of the information that corresponds to a person does make 2 disjoint persons.
Like running a different seed on procedural generation, entropy will ensure that these two identical persons won't be identical after whatever ticks in the biological clock.