My Begonia has large rhizomes that overlap on top of one another. Will this hurt anything, or should they be separated?
It won't hurt at all. Usually the older rhizomes will eventually dry up and fade away much like iris rhizomes. It's probably a good idea to refresh the pot every few years or less.
My neighbor gave me a Begonia with overgrown rhizomes like that. I broke them up and put more space between the pieces when I repotted, and had enough for 2 larger pots. A few of the pieces didn't take but most have more spots where they're sprouting foliage now.