The only way to know for sure is to let the battery drain completely. Then recharge it completely, load up a game (preferably one that has a demo mode or an opening video that will play over and over again -- I don't know if the NDS can experience screen burn-in but better safe than sorry), close the lid, and time how long it takes the battery to drain completely. Then recharge completely, load up the same game, and let it run again, but with the lid open (whatever backlight brightness you normally use) until it drains completely.
I'd be surprised if the backlight doesn't cause the battery to drain faster than no backlight when the lid is shut.
-Bri