The problem with using any kind of rechargeable battery as a voltage regulator is that you can vercharge and destroy the battery, so you'd probably want some sort of regulator in there anyway. It would be nice to actually fit a battery charge circuit in there, say some off-the-shelf Maxim chip, but that complicates it a bit.

Also, yeah, regular NiMH batteries lose something like 1% of their charge every day, but there are newer "hybrid" NiMH batteries that, while being rated as much lower power, lose only 15% of their charge annually. I've bought some sets for my occasionally-used flashlights and headlight.