It’s a matter of neutering and age. My rabbit Bobby has free reign of the house (except the rabbit room where I keep my 3 senior rabbits) and he’s very good with his litter box. I think Bobby is about 3 or 4 years old – not sure of his age as he was dumped off at a guinea pig rescue and the vet just made some guesses to his age.
Initially I just had him in the cage they dumped him in but once my other free roamer, Pepe, passed away, I decided to give Bobby a chance at free roam. He’s very good – he doesn’t chew on anything (maybe because half of his teeth are gone and he’s older).
I have had some rabbits though that were just too destructive for free roaming and would destroy my house in a second if they had the chance.
So I guess it would just really depend on the rabbit. I guess I would say, get him neutered first and then slowly introduce him to the rest of the house. Not sure how young Rory is, but young rabbits can be a little less disciplined than older rabbits since you mention the peeing on the bed and such which is typical of a young unneutered rabbit.