Perhaps I should've said "wristwatch formfactor", you're right, battery performance would not approach cheap digital watch, not by a long shot. But at at 120mW, you'd be able to get a few hours out of it with a CR2032 cell, which is better than useless. Garmin made GPS wrist units that up until recently have done no better than this, although admittedly, there's probably more utility in having a GPS on your wrist than an atomic clock.

Your could write "HOURS AND HOURS OF BATTERY LIFE!!" on the packaging.