Unfortunately, the answer to this is not a blanket yes. In some cases, RV air conditioner units can definitely be run using solar power. However, if you have the most basic RV solar systems installed, the answer is probably no. That being said, most RV solar kit manufacturers will maintain that their solar panels have the capacity to do so.
The reason being is that for air conditioning to run efficiently from RV solar panel kits, some modifications to the systems need to be made for them to have this capability. To make this possible, the solar power has to go through the charge controller and then into the battery bank as normal. It needs to be turned into AC for it to power the air con, so an invert is needed. Not all kits will come with an inverter.