It does depend on the Inverter. My stock Inverter was a Xantrex XM Pro 1000. I could turn it On or Off when needed.
I upgraded to the Xantrex Freedom Xi and it will power on as some as shore power is plugged in. It can only be turned Off or On when there is no shore power.
I have since required the way my Freedom Xi Inverter works so I can turn it off even when plugged into shore power.
__________________
|