The RV (and any other electrical device) doesn't really draw current. Current flows depending on the load applied in accordance with Ohm's law. In your case, it would probably be on the order of a couple or three amps assuming you're correct about the load (i.e. the fridge isn't on AC power, and there's no electric water heater or space heater in play, and so forth). The RV is basically just acting as a power strip in this case.
The concern here is that there's nothing preventing the circuit from being overloaded accidentally if the breaker doesn't work properly. The RV would not consume more than 30A due to the main breaker in the RV's panel. If there were a short circuit somewhere before that breaker, the current could be higher. 30A on a 15A circuit (and particularly through a possibly worn 15A socket) could cause things to get pretty warm.
