Games : Will my game hold a save even without a battery as long as the system's still turned on?

So I've been wanting to back up my old Pokemon Red game (or at least save my team) and I'll have the means to do so within a few days to a week. The save battery still works fine, but I'm a little paranoid that it'll decide to finally die on me before I can make my backup.

I know that save files only last for as long as the game has a power supply, so once the battery dies they're gone forever. But if I were to leave the game running on a Gameboy SP that's plugged into an outlet and constantly charging, then would by save file be fine even without a working battery? (At least until I next turned off the system, of course.)