The length of the extension cord will make a difference, but a 12 awg HD cord should work. If only a tv in use, and as mentioned, converter not working hard, it should not be a problem to run fan only, on the AC.
You can buy a voltage indicator that simply plugs into wall receptacle to monitor available volts, or use a meter to test if you have one.
Keep in mind, if plugged into an outlet in garage, or house, is there more electric draw on same circuit, as well as the RV?
Jerry