No, it's The No No Song by Ringo Starr. It was actually written by Hoyt Axton, who also wrote Steppenwolf's The Pusher (today's bit of musical trivia).
Dunno. Here's a clip. I can't claim to be an exhaustive Frank authority, but I've never heard an FZ version. Then again, FZ quoted so many many many different things all through his music, it's extremely possible he threw it in somewhere.