Since the OP was asking about keeping his batteries charged, the answer is YES it is advisable to keep his coach plugged in to a shore power outlet.
That being said some inverter/chargers will not charge BOTH the house and chassis batteries when plugged in to shore power. He may need an additional battery charger to take care of his chassis batteries.
When the coach is sitting there are several parasitic items that will drain your house and chassis batteries, depending on how they are wired. You will have the CO detector, the propane detector, the smoke detector, the radio memory, satellite boxes, etc.
Keeping your batteries fully charged is the best way to prevent them from freezing during the Winter, unless you want to remove them and put them in a warm location.