I recently destroyed the screen on my phone making it not possible to interact with it, so I've removed the sim and put it in a cheap feature phone. It still connects to WiFi (can't turn it off if I wanted to) and it beeps to let me know I have an e-mail. I can still listen to podcasts because my podcatcher automatically downloads and queues episodes and my headset has playback controls, and I have been using it for that purpose as much as I always have. Now when I go to bed, the battery icon has only the tiniest sliver empty; I expect it would last at least 4 days without plugging it in.
I think that it's safe to say Android OS is not draining my battery.