Rv setup - will inverter run the battery charger?

[Hedges]

It’s a good point. The all in one has earth to the inverter, but not back out from it. There is a ground point though.

But does the inverter internally tie neutral to ground all the time? Only when AC isn't present on the input? Never?
I hear that inverters intended for shore power connection have a relay to ground neutral internally when operated stand-alone, but isolate it when plugged in (so neutral and ground aren't parallel paths for current when plugged in.)

I'm mounting a Sunny Island inverter on a truck, so what I will do is wire an outlet with neutral shorted to ground, nothing else. When not plugged in to the grid, I'll plug the cord in to that. Manual switching of neutral to ground.