I'm not so sure about that. There
is a battery in the G6, which as far as I know is used to hold saved games until you next reboot or switch on the DS. So if your battery is low and you save a game then switch off, your save might be lost. You'll be ok if you soft-reset to the G6 menu or quickly switch off and on again.
See the What's going on with saves?, Need to restart G6 Lite now? thread
http://gbatemp.net/index.php?showtopic=34837