Did the Beatles Record Mrs No?

The Answer is No

Not even during the Get Back/Let It Be sessions

The Beatles did not record a cover of the Joe Cocker song "With a Little Help from My Friends" during the Get Back/Let It Be sessions. The song was originally written by John Lennon and Paul McCartney and was released on the Beatles' 1967 album Sgt. Pepper's Lonely Hearts Club Band. Cocker's version of the song was released in 1968 and was a hit single in the United States and the United Kingdom.