A voltmeter is your friend (use as described above) however here is a guideline.
IF you have a really big (#,#00 watt) inverter,, AND it is also your charger.. ODDS are it connects directly to the battery BEFORE the disconnect switch so yes, it will charge JUST THE HOUSE batteries.
IF you do not have a thousand watt plus inverter Odds are the converter/charger is on the HOUSE side of the disconnect and thus will not be able to charge unless the batteries are Connected/Use/ON mode.
BUT.. Here is how to find out..
Unplug for liek 30 minutes.. Measure battery voltage AT THE BATTERY (should be12.6)
Plug in for 10 minutes,, Re-measure 13+ indicates they are charging.
