Very likely yes. I have a less than ideal service to my shop and am able to run the AC on all of the campers we've had off of a 15A service.
But at some point (may not have been the camper AC) that outlet got hot.
I replaced with a 20A outlet (since it is only a few feet from the subpanel, and already on a 20A breaker) and that works like a charm.
Keep the extension cord short. If you're using just your RV cord with no additional extension cord(s), that is the best scenario.
Worst case, it pops the breaker feeding that outlet. No harm, no foul.
