Probably yes, and with no problem, as long as you are not running anything else, like electric on your water heater, microwave, hair dryer, televisions, toaster oven, electric frying pan ... all at the same time.
Simple test? Plug your camper into your home wall outlet. Homes are usually 15 or 20 amp circuit breakers. Make sure nothing else in the house is turned on with that circuit. Now power up your RV. Flip on the air conditioner. It will run, no problem, as the amp draw is far less than 15 or 20 amps. Now flip on your water heater. Now flip on that hair dryer. When you reach the 15 amps, the breaker in the house will trip. There you have it. You know where the limitations are. But yes, the air conditioner by itself will run with no problem on 15 - 20 amp circuits, but everything else might not. Try it... see what happens at home. Then you'll know.