No. The song was written in 1963 by Chicago native Allan Sherman along with Lou Busch. The Leonard Skinner of Lynyrd Skynyrd fame was a gym teacher at Robert E. Lee High School in Jacksonville, Fla. who "tortured" his long-haired students, among them Ronnie Van Zant, Gary Rossington, and Bob Burns, who would go on to form the band.
From a 1977 Associated Press feature about Lynyrd Skynyrd:
"It seems a physical education teacher named Leonard Skinner didn't cotton to long hair or loud music. A run-in with him helped get the boys suspended. As a way of getting back, they named the band for Skinner, changing the vowels to avoid a lawsuit and becoming famous enough to make the story a rock legend."