GFCIs will not trip due to open ground connection; if they did, you could not plug in any appliance with a two-prong plug to one.
They will detect and trip for leakage to ground even if the ground wire is disconnected. Obviously that leakage won't be going through the ground prong of the RV socket, but it could be going through your body to ground if you're standing next to the RV, for example.
A GFCI is the only way per code (so far as I know) to install a three prong outlet in an electrical circuit that has no safety ground. Such receptacles must by code be marked to indicate that there is no grounding, however.