No it does not hurt the AC or your camper. It will limit what else you use on that same circuit so expect the CB to trip during heavy load starts. I had in the past ran my AC in our camper from a standard 20 amp circuit for several years before installing a 30 camper outlet last year. I'd forget about it and load up the same circuit with my table saw when the CB would trip. Just don't use an extension cord unless it is the same size wiring as the camper. I've used a 100 foot extension I made up and had no problem where I couldn't get closer to the outlet when visiting my brother.
If you want to use it for any length of time other than prep you'd be better off adding a 120 volt, 30 amp circuit with out door outlet.