THe answer depends on the converter you have..
The old Magnetek 6300 series and I suspect some of their other entries had very poor voltage regulation, also they were designed for 110-115 volt not today's 120 volt. so they tend to overcharge the batteries if left plugged in long term and "Boil" them dry in very short order. Flip side. the 6300 needs a battery connected or it does not work properly.. (may run lights ok though).
More modern converters have better regulation and with those, if you have "Shore power" (House power) leave the batteries connected.
I have a Progressive INdustries Intella-power 9180 with optional wizard.. I keep mine connnected save when re-filling propane tank (Easiest way to turn EVERYTHING off).