[folivier]

The inverter has a pass-through so if on standby and on either shore power or with generator running the inverter is not running. If power goes out then the inverter will automatically switch from shore power passing through to running off of the batteries. Just so that you know this will keep your refrigerator running but will run down your batteries after a period.
Keeping the charger on will keep a float charge (once batteries are fully charged) on your house batteries to keep up with any 12 volt loads such as your lights.