Actually, it may be possible to code something similar to those GBA games freeze states or whatever. That is, basically shut down all hardware and severely underclock the cpu and put it in an idle state waiting for a button interrupt or something like that. That way, you just leave your gp32 on at all times and it basically drains your batteries really slowly. I'm not sure how long the batteries would last, but it should be at least a few days. Not certain though. I'm imagining you'd turn off the video and sound hardware from software, and clock it down to like 10mhz, if possible, the only things running being the timer code for the clock, and a button interrupt, so you could re-activate the sucker.
It should work, but the only limiting factor would be how long the batteries would last, and that's directly related to how low you can clock the GP32.
Oh well, just an idea.
P.S. Darkfader's project with the clock worked for a while, but then burned out the clock part. So it's got some major problems. Scrap that idea.