Lead acid batteries get an extended life if they are kept cold. During the spring/summer/fall charge it overnight every 30 days. Self-discharge slows the colder the battery is so you can get away with doing it only once in the middle of the winter.
Since you'll be leaving your camper plugged in you'll get the best of both worlds - extended battery life since they'll be cold, and no need to remember to recharge. I agree you should check the water level often until you are sure your converter isn't boiling it off.
2008 FR Salem 26TBUD
2010 FR R-Pod 171 (2009-2015)
2010 Chevy Suburban
Honda EU3000is inverter-generator