It is just a small drain on the battery, but yes, over time it could kill the battery. You may have a battery on/off switch located next to your battery. I know our unit has this and if it is going to be unplugged for an extended period of time, I shut the battery drain off. I put in a 30 amp outlet out in my back yard so we can keep our unit plugged in all the time. Even use it sometimes on the weekend if we have an overflow of company!
2010 Jayco Quest G2(SOLD)
2014 Jayco Eagle 33.5RETS
2007 Ram 2500 5.9L Cummins(SOLD)
2015 Ram 2500 6.7L Cummins 4WD