I've shot a G2 since the year 2000. Never took the batteries out except to replace worn out ones. I would not be taking yours in and out if I were you. More chance of crossing the threads on that battery cap than a chance of the LCD bleeding I think. Just leave them in.
Congrats on the G2. Welcome to the club. The 45 is easily the SHARPEST and most 3-D effect lens I've ever used.