I'm very pleased at the battery performance on my gripped 5D3. I've never drained them, but at present, with over 1200 shots on the current charge, one battery is at 58% and the other at 54% (genuine Canon grip and batteries). That's with a 580EX II flash used on about 1/2 of the shots. I also keep the LCD on to show each picture for 2 secs...Just to make sure I got the exposure I wanted. I'm shooting almost 100% in manual these days, so that may save some battery power as well. For what it's worth, my gripped 60D and gripped 30D typically gave me 1600-1800 shots before shutting me down.
As far as Eneloops in the flash, I've only drained them to the point of 2 second or so recharge on the flash, and that was perhaps 600 or more flashes. But just in case, I always carry a spare set with me. If I were planning on a full-day wedding, I'd definitely have 3 sets...one in the flash, one in my pocket, and one in a charger.