Yes, inverter get's 12V directly from house battery. Even "off" there may be a slight draw to keep the "on/off" circuitry energized. Only removal of the big inverter fuse (next to house batteries) or disconnecting one of it's leads will ensure that there is no draw.
There should be a schematic on the inside of the compartment door.
Best thing is to have a battery tender and if that is not an option disconnect the negative leads from the bank or remove the two big fuses. (one house, one inverter).
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2020 RAM 3500 DRW Long Horn. In the hunt for a Palomino TC, formerly a 2017 Berkshire 38A: https://dragonship.blog/
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