If we're going to get really technical, they have an extremely, EXTREMELY small chance of existing, and not even in the same way. There was a movie I watched, the name escapes me, about a guy who has the ability to travel through time thanks to his family. He saves his sister from being crippled in a car accident and then later goes on to impregnate his wife. The child born of this is a daughter, instead of a son like he had before the trip because a sperm wouldn't make the same trip after a few hours or days.
The whole time travel shib doesn't make sense if someone disappears, but the memories don't.