They remember being themselves

You don't know that until you've actually done the experiment. Some parts of memory may be "passive" - encoded in the configuration of neurons and synapses - while other parts may be "active", dynamically encoded in the electrical stuff and requiring constant maintenance by a living brain. To take an example we understand well, turning a computer off and on again loses all sorts of information, including its "thread of consciousness".

EDIT: I just looked it up and it seems this comment has a high chance of being wrong. People have been known to come to life after having a (mostly) flat EEG for hours, e.g. during deep anaesthesia. Sorry.