My house has one GFCI outlet with five regular outlets strung along with it, any of which will trip the GFCI. Seems like any outlet you connect will be GFCI connected.
Usually though when you connect to a 15 amp outlet on an inverter, you are capped at 1500 - 1800 watts and to get the full output of The inverter, you need to hardwire it. My 2000 watt inverter was limited to a 15 amp plug, but hard wiring I’d get full output; my 3000 watt inverter is limited to a 20 amp plug, but I can get the full 3000 watts from hardwiring it.
In my case, hardwiring is no longer GFCI.