Last year on the way to Florida we stayed in Cabelas with our older D/A Chevy and I disconnected the trailer, turned out next morning it poured rain so we stayed another day.
During that rainy day we used our invertor to run the Television, fridge running, cold as it was 1st of November so we had the furnace on.
We left the next morning and I checked the battery gauge in the Trailer, we were down to between 1 and 2. The point being if we had stayed plugged in would it have affected the TV batteries?
I really don't know but I don't want to find out.
Thanks to everyone for weighing in with their opinions, you all are helpful and we really appreciate your input, Bon Voyage to one and all!
