But, yes, the battery should be fully charged before updating the firmware. It's not strictly necessary, but I can't tell you how much charge you do need, and there's no reliable way to measure partial states of charge. Much better to play it safe. (And I always go belt-and-suspenders, and plug the charger into it after the USB icon shows up...)
Of course you'll "need" to upgrade your N800 to Diablo at some point... but I doubt it will help with your router lockup issues.