No, the song, written and performed by Harry Nilsson (released on Aerial Ballet in 1968), is officially called "One" and has been covered by several artists, including Three Dog Night, Johnny Farnham, Aimee Mann, Filter, and Chainsaw Kittens.
The Beatles became fans of Nilsson after being given copies of his 1967 LP Pandemonium Shadow Show by their press agent Derek Taylor. The album included a cover of "She's Leaving Home" and a medley featuring "You Can't Do That" interspersed with other Beatles songs. Nilsson recalled they each called him one by one to express their admiration of his talent. In the interview clip below from May 1968, Lennon can be heard exhorting, "Harry Nilsson for President!"
One of Lennon's favorite tracks from Pandemonium Shadow Show was the album's closer, "River Deep - Mountain High", a clip of which can be listened to below at 2:00: