Yes it would work in an RV, and the real reason is because it's 120v and less then 15amp draw. It will wash and dry clothes just fine given time. Which if you're doing laundry while RV'ing it is more then likely because you are retired and living on the road.
Nice unit like that I would start at $500 and see where you go from there. Don't know if I would put it in the RV section though. Lot's of people have cabins, apartments, or small homes where space is at a premium that would like something like that.