There are several differnt ways invertes are installed. A couple of different types and a couple of on /off switches..
Now some RV's have a small inverter for TV /RADIO use. this likely is a pass through model designed to be left on all the time (unless the RV is in storage mode) it goes into "Standby" if shore power is present
Some may have a 'Stand alone' inverter that only makes 120 volts out of 12 nothing else. no pass through Turn off if not needed.
I have a Inverter Charger (my 2nd)
The first on had a master ON/OFF/Remote Switch (The big red one I call it) and if this was OFF or if in remote and the remote switch OFF it was OFF! and I Mean OFF and nothing down line worked NO battery charging. NO power to loads
THe new one .. I'm not sure what happens if I turn it off (have only done it once by accident) if you have shore power (I did not at the time) but since it too is an inverter/charger I leave it ON all the time..
BANG NO POWER (Car hit that big stick just outside the RV park and down came the power lines).. Televisions and computers did not even blink.. THey never knew iot because the inverter is in UPS mode and kicked in instantly. When power wa restored the box outside went 1-2-3--171-172 CLUNK and the inverter went back to Standby mode and once again TV's and Computers did not even blink.