No, Lennon really liked it, it isn't an example of his sarcasm.

McCartney has said it was inspired by concern for Lennon's first son as Lennon's first marriage broke up. Lennon interpreted it as McCartney coming to terms with changes in their (John's and Paul's) relationship and wishing for John to find happiness however he could.
Lennon also liked the "anthem" qualities (note Lennon trying for anthems of his own with "Give Peace a Chance", "Power To The People" and to some degree even "Instant Karma", and "Mind Games".
McCartney also reports Lennon liked the obscure line "The movement you need is on your shoulder". When McCartney demoed the song for Lennon he said he'd change that one since it was nonsensical and Lennon said "Don't---it's the best line in the song."