The gen set will not idol down if it is hooked up to the power cord, it has a constant pull on it from the rv's inverter. As for the over loading it should not be unless the ac is on or trying to run.
Some think that the Honda 2000 will run everything except the A/C....wrong !!
It won't even run the microwave,...if the batteries are dead ! (60 amp conv)
Rich
'98 Flair, 454, Onan Microlite 4k, Intel PD 9155 w/ wizard, Sta-power 1500 watt Inv, 2 6v batts, ammeters, KingDome/sat, Oly Catalytic Heat, hauling 2 Bent Bikes and sometimes towing a Tracker F&S boat.