The point you bring up is a good one. Your inverter can be enabled for pass-through or "by-pass", which will let AC current in and energize the inverter outlets with AC shore power. The trick is to NOT have the inverter enabled on stand-by mode. You don't want your inverter to kick ON when you lose shore power, since your small electric heaters would deplete the battery bank in no time. Our general rule to clients is only turn ON the inverter when you need it and OFF when you don’t.