Various recordings with Best on drums have escaped over the years - the two sessions made in Hamburg under Bert Kaempfehrt backing Tony Sheridan, the Decca audition tape from January 1962, the Parlophone test session from June 1962 and a some BBC recordings made in Manchester. Best's drumming is very unadventurous, usually the same predictable shuffle rhythm. On the Parlophone test recording of Love Me Do his timing during the bridge section is awful - no wonder George Martin wanted to use a session drummer.
When four of the Tony Sheridan recordings were issued in the US by Atco in 1964, they over-dubbed the drum parts. This is probably behind Bernard Purdie's claim to have drummed on some Beatles recordings, as he was on a lot of sessions made by Atco's parent label Atlantic at the time. Atco also put out an album, using cover versions of Beatles and other Merseybeat hits to fill it out, which Purdie may have also played on. I've also heard talk that Brian Epstein hawked the 1962 Decca audition tapes around New York in 1963/1964 to try and get them released, and may have got Purdie to over-dub drums on this session too.