No problem. Yes, you do need to remove the RMR to change the battery as access is on the bottom of the sight. I would say you will be very close to re-zeroed with a shotgun but I always check my zero prior to the season starting. Also, battery life is a long, long time especially on a turkey gun. I turn mine on when I start working a bird and off when I move. So years of life is normal.
Let me know if you have any other questions. DD