if an Inverter is 'wired' into the Main breaker panel, then it's usually to only one or a few circuits. They will work even when on gen or shore because the Inverter has a 'pass thru' of 120v power via a built-in relay/auto transfer switch. And, yes, any 120v power from the gen or shore power is NOT to the inverter, but to the CHARGER, though many inverters then allow this 120v power to 'pass thru' when the inverter is not needed.
if the inverter is a separate device, not wired 'to' the Main breaker panel, then any item/device/outlet that is powered by it will come directly from the inverter, and some of these inverters also have one or two outlets on the unit itself, just as a simple way to power plug-in items. These items will continue to be powered by the inverter EVEN when you are on gen or shore power, because it is the ONLY power they receive. Your Converter/Charger will be recharging the batteries, during Inverter use, while on gen or shore power.
and, it could be that they simply used the same circuit breaker to feed a circuit of outlets(3a), AND the Converter/Charger at the same time. If you turn off this circuit, you would lose those outlets, and the battery Charger.
But that would then make it sound like only the GFCI circuit outlets are powered by the Inverter(?)...
could yours be different? sure, factories do weird wiring sometimes.
crazy, but fun.
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