My TI-89 has that kind of batterylife but it uses four AAA-batteries.
You could call it a pda:-)(newest models even has a built in clock) but it really is a calculator with a 12Mhz 68000 and 256KB ram.
And No it won´t run AROS as nobody could get Linux to work! :-)
Probably this have something to do with the unavailability of MMU in the 68000. Installing Linux on Amiga requires MMU equiped Amiga. I think you will have hard time implementing multiuser, memory protected OS without MMU. This was one of the reasons the AmigaOS wasn't built with memory protection in the first place - needs to many resources for MMUless CPUs. (68000,68010 and 68EC020).