Running the RV generator to recharge or keep house battery charged depends somewhat on the design of your converter charger. Recent designs may have fast charge rate capability built in. Older designs had quite slow charge rates to protect battery from over-charging while rig is on shore power or when generator is powering the converter charger. You can check the state of charge in your house battery with a simple voltmeter when generator is shut down and engine is not running. You should get a reading of over 12.6 volts with fridge, etc. drawing current with fully charged battery and 13.6 volts with RV generator running, and around 14 volts with truck engine running and RV generator shut down.