Very back of the envelope, based on what we know about MiniDisc players. Everything very approximate.
Assuming UMD is no more efficient than MD, here goes:
MD is a mature technology ~ 150MB
For a modern netMD:
66kbps gives 50 hours on one AA battery ~ 2000 mAh
so
1.5 min / mAh
1 min = 9000KB uncompressed = 150KBps = 1200kbps
1200/66 = 18.18:1 compression
so throughput for netMD is 495KB / min (9000KB uncompressed/18.18)
which gives
742.5KB / mAh (495KB * 1.5 min/mAh)
on the equivalent of 2AA batteries that's ~ 4000mAh = 2.83 GB transferred on one charge.
Not shabby. Certainly enough to play games without the drive being the battery killer. Yeah, it's probably a best-case scenario, but at least it's a baseline grounded in something we know as fact. Anyway, we'll know the truth soon, so this is sorta irrelevant.