Yes the refer needs a source of 12 volts in order to run, even on 110 V AC. The12 volts operates the control board. By having your RV plugged into the shore power the convertor is charging the house battery that supplies the 12 volts to the refer, it also charges the battery/ies so what you need to do is keep a good watch on the water level in the battery about once a month. The convertor should not do any damage to the battery as long as it does not boil all the water out of the battery and you keep the water level up. You might want to check what brand convertor you have and if it is indeed a 3 stage charging convertor as stated in many above posts.