Welcome ASHORE? =)
The heater fan pulls some serious power. The heater and water heater have electrically operated GAS solenoids... along with the control board power draw.
I left my 34' AS unplugged for 2 weeks, doing cleaning and basic maintenance with using lights and water pump and the voltage on the batteries dropped to 12.4VDC.. so, the circuit boards don't pull power when they are switched 'off'...
Yet, I have run the heater overnite on battery.. but, here in Texas we had the heater cycling on/off.... not continually running. It put a dent in the batteries and took about 6 hours to fully recharge on the new converter.
If you are plugged in to AC, then the Converter will supply the power needed in your camper, even with all the stuff running... or, it is supposed to. I have a multi-stage converter.. after market, that meets all the needs quite nicely.
So, the only way you are likely to 'run down' the the batteries would be if you are 'boondocking'... with no replacement electricity.
Running heaters is a great option if safely used... watch for Oxygen consumption and CO output... the combo is deadly and we lose a few folks a year who misuse the devices... as a prior mariner, you probably are aware of the risks..
You can get a small generator to supply enough power for the converter to recharge.. if allowed in your camping area. Exhaust must be properly monitored as well as theft of gennys occurs often..
Others use larger battery combinations and solar resupply methods...
Enjoy the journey... and the motion of Aluminitis...