Ground pin is a safety device. It is not required for normal operation because it does not conduct current in normal operation. Ground pin of every appliance: fridge, stove, microwave, drill, saw etc. is connected thru green wire of the cord to metal parts of chassis & metal cabinet that is hold & touched by people. When plugged into wall receptacle, ground pin continue thru bare uninsulated wire of house wiring into distribution panel where it is bonded to neutral and actual ground rod driven into the ground. So every electrical appliance's metal cabinet/enclosure is at ground potential and a person standing on ground and touching any (grounded) appliance can not be electrocuted. Should there be electrical fault and enclosure/chassis should get hot for any reason, there would be instant short thru ground pin wire to ground and circuit breaker powering that circuit would open cutting power to said appliance. This is the only time when ground pin actually conducts current. Exactly same protection should be expected from an inverter powering any appliance in an RV. Any inverter that uses ground pin for any other purpose is defective in my book and should not be on a market. I had one of those a few years ago and I promptly destroyed it by trying to hardwire it into RV electrical system. If your inverter output does not check exactly same with a plug-in tester as in house outlet, get rid of it.
The inverter OP is asking about is a good one. I have two 600W versions.
