Nah. Nook Simple Touches can be rooted and run Android just fine. As long as wifi is off (thus disabling the vast majority of app background syncing / periodic updates) it easily lasts a couple weeks. For that you can run a surprising number of apps just fine in a ridiculously-limited available RAM space. I can't imagine this would be anywhere near as slow as a NST, so it should be able to do just about everything except play 3D games and visit crazy-bad websites.

As long as you don't busy wait and only update the parts of the screen that change it's not too hard to write software which doesn't impact battery life too much.

EDIT: To add, obviously minimise network connections. And if you do need them, batch them.

The test model I used for a month only needed one charge, it works a lot like the black and white kindle and the document stays static on the screen and the device only really turns on when you write on it or turn pages.