Charging via towing would likely cost far more than paying for grid power. The MH would burn significant extra fuel to drag a car that is resisting being pulled. As far as I know, no EV has this capability and I wouldn't expect it in the future. It's way too small of a market.
Technologically, you can certainly plug into the pedestal. Depending on which outlet and the charger on the car, it will vary how fast it charges. If you offer the owner to pay extra for the electricity and unplug if the park grid is maxing out (hot summer weekend when breakers start popping), I wouldn't see any complaints from the owner. Try to sneak it and justifiably, you might wind up with an angry owner.