I think so, because the Beatles have covered other Little Richard tunes and he was one of their personal favorites. But to find a record collection with that cover song by them seems like a difficult search. But it pops up on the internet. Have you had any luck yet?
I became interested in the version after seeing the film Backbeat, but with the Beatles I still have not found on the Internet, it would be great to find the song with the Beatles for download.
At one of the other pages, someone said they did it for the BBC, but I don't know about that. My guess would be the Get back sessions. Either way, I'm near definite that they performed it - even recorded it; I'm just not entirely sure where or when.
