I have an EMS that will not let the AC work if the voltage is too low. That said, it is easy enough to check. Using the Kill-a-watt meter, you can plug it in to the shore power outlet and then plug your coach in. This will give you the voltage drop and the amps being used. This will let you know if the wiring is sufficient to supply the voltage and amps necessary to run your AC. The onlt way to check the pedestal outlet is under a load and this is what you accomplish by using the Kill-a-watt meter.
When we are hooked up to 120 volts, I always make sure that my inverter/charger is turned off so that the charger is not drawing power. I also put the water heater on propane.