A definite no. The original version was written by a friend of
his called Sonny Curtis who joined the Crickets and released the
first version after Buddy's death.
The song was later covered more famously by the Bobby Fuller
Four and the Clash.
The Crickets version with Sonny Curtis (recorded months after
Buddy's death) is often mistakenly credited to Buddy Holly and
included on his greatest hits albums despite not featuring on the
recording at all.