It should not matter particularly that it's left on, and with a good converter would probably be better for the batteries particularly in a warm climate where the batteries will tend to self-discharge fairly quickly. Do check the water level in the batteries from time to time if they are flooded batteries (and add distilled water as needed).
If you have a solar setup and some sunlight where it's stored, disconnecting from power would work well and you could still use the lights etc. from time to time.
(If it's level, an RV fridge is not harmed in any way by running it either, although running on AC power it is very much a power hog compared to a standard residential fridge.)