It depends upon the circumstances.

Have they had intense auras in which they strongly recall these same things happening in their life? I've experienced that MANY times in my life ~ I could have sworn that I was psychic and dreamt years before of these things happening in my life now. Those turned out to be a common beginning of complex partial seizures. Not crazy there.

I am skeptical if their belief is that they were a powerful, well-known person in history. No one ever seems to convince themselves that they were living centuries ago, as a peon slave. That's where my skepticism comes in.