I would NEVER leave one of my own rabbits overnight, just because of that. It's hard enough to get them eating again at home without adding the extra stress of being in a strange place. I would only do it if there were complications and emergency vet care was needed.
I just had one of my buns spayed and spent most of the evening and night trying to keep her warm, because of how cold they get from having a GA. I can devote all my attention to the care of my bun, and I don't know that a vet office would pay as close attention to the needs of my rabbit as I would. Not to mention that I also know my rabbits behavior a lot better, and would be able to better tell if something is wrong. They would do the general stuff like syringe feed if needed and give pain meds, but that can all be done from the comfort of home.
Maybe for a new rabbit owner, or if someone has no experience with neuter/spay after care and is uncomfortable with knowing how to deal with it and get their bun eating again, then maybe overnight vet care might be better. But home is really the best place for them to recover. Plus this is something you already have experience with.