yes, it all depends on the converter/charger..... a multiple stage high amp charger (something similar to the progressive dynamic charger/converters) can be plugged in full time when connected to a battery... and this will also allow for a a couple of small heaters with a "freeze-proof" setting to be kept plugged in all the time, to keep at least a minimum of heat around the plumbing areas when the temps drop down to freezing.
a quality multiple stage charger can significantly increase the life of the battery over what you will get when using a single stage unit...