First, this has nothing to do with the AC unit.
Second, you need to find out what make and model of "charger" you actually have. It should be a "smart" tender type battery maintainer and NOT a cheap trickle charger.
Then, you need to invest a few $$ in a multi-meter so you can test things like this for yourself to be sure.
So....to get anything near to a good answer, more information is needed.
'07 Damon Outlaw 3611
CanAm Spyder in the "trunk"