I didn't even have to search for the local files. iTunes had a nice "Show in Windows Explorer" button next to the episode I downloaded, which opened a directory with the mp3 audio file for the episode (neatly tagged and named and all). I opened it with VLC and confirmed that the playback works perfectly fine.
Disclaimer: I haven't tested the part with transferring the file to an Android device specifically. But if an mp3 audio file plays fine in any third-party media player on Windows, I think it is safe to assume that it would play fine on Android as well.