I'm sure there'd be some way to have a clock. PCs (and the Nintendo DS) are able to accurately know the time even after they've been powered off for weeks. Perhaps it would have to be part of the firmware to actually utilize a small bit of battery while the unit is off to keep the clock going, but I'm sure it could be done.
However, it wouldn't be the greatest app, though, due to how long the GP2X boot is, plus navigating to the actual clock app. A calendar wouldn't be a great idea, either, since there'd be no real easy way to add appointments (no keyboard = hard typing interface.) Perhaps if a USB/EXT keyboard comes out, but even then, you still have the load time issues.
Good idea, but like Shikaku said, the GP2X isn't a PDA, it's an entertainment device.
Stop trying to make my toy useful. ;-P