I use my Honda 2KW Generator all the time with the OFF-ROAD POPUP trailer RV30A shore power cable plugged into it using an adapter when we are camping off the power grid.
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I have all the 120VAC breakers turned off on the 120VAC side except the receptacles around the trailer and the on-board converter/charger unit.
My 12VDC items including my interior lights are running off the batteries during this time...
The only reason I use my 2KW Generator is to recharge my battery bank once a day starting at 8Am in the mornings. This will take about three hours of generator run time to complete a 90% charge state for my 255AH battery bank.
I will also make some fresh grind and brew bean coffee for the day stored up into a thermos carafe while running the generator which is only drawing power for about 5-minutes...
Roy Ken