I keep mine unplugged and it gets surprising good battery life, and I think it kinda improved with the downgrade. On normal use I would get like 8-10 hrs screen on time. No spicy pillow yet, though I did have that issue with my old iPod.
My old iPad lasts weeks on its battery if I don't use it, I can only imagine it actually sleeps and would not answer network requests in this state.
Congrats for the successes :-)