That may be. IF the unit can pass SHORE power then the GFCI would be indicated.
THe job of the GFCI is simple.. IT measures current in both the black and white leads. if they are the same, it is happy but if it detects more current in the black than the white.. CLICK and darkness happens.
Mains power (Shore) the neutral is bonded to ground. so if there is a short between the hot lead and the case of the device you are holding.. YOU become a return path. the GFCI reacts so fast you won't even feel a tingle.
BUT the inverter... is not normally bonded to ground.
