Maybe. 3.3V probably wouldn't be enough to charge, 12V would be too much unless you had quite a few cells. Depends on the number of batteries, really. If it was one cell, 3.3V would be enough. Most probably use 2 or 4 cells, so you would need some sort of charging circuitry. Remember that the N64 would only charge it while on.
I think the AVR+RTC completely homebrew way is the way to go. You could have the battery backup to keep time, then when you put it in an N64 and turn it on, boom, clock. Of course you could do other things with it, too. Maybe a cool light pattern? I wonder if there would be space to cram an appropriate game into the cartridge.
Hmmm.