If I update to the current public beta of iOS 10 right now, will I be able to update to the official release when it comes out without having to downgrade back to iOS 9?
I'm not really certain that the final beta is usually the GM that is the pubic release. Perhaps I'm off in my recollection, but I think that basically sometimes that's the case, but other times it's not. But, yes, in either case, there shouldn't be a need to downgrade.
You can always put the latest official release of iOS on your device, no matter what you run on it at the time. You can also unsubscribe from the beta programme at any time, so no particular inconveniences there.