I think the short answer is no, but there have been some honorable mentions. Apparently Vince Sr. had a chance to sign Andy Kaufman before he popped up in Memphis and turned it down. Up to that point, Kaufman had never stepped in the ring and was known predominantly for "Fridays", "SNL", and "Taxi." It's supposedly one of McMahon's biggest regrets. Mr. T gained plenty of celebrity in the 80's with "Rocky III" and "The A-Team". That success launched him into the WWE While he was never a full time wrestler, he did plenty to publicize the WWE in the 80's, worked two Wrestlemanias, and dipped in and out of sports entertainment on multiple occasions throughout his career. Similarly, Tom "Tiny" Lister Jr. also dipped in and out of wrestling after starring as Hulk Hogan's opposite in "No Holds Barred", but it could be argue he found more success as an actor after his biggest run in sports entertainment in movies like "Friday" and "The Fifth Element". Of the names listed he's probably had a longer go of professional wrestling and still takes the occasional indie booking.
Then there are the independent wrestling outliers like David Arquette, Stephen Amell, Johnny Fairplay, and Dennis Rodman who never worked for WWE but have pursued careers in wrestling, especially Fairplay and Arquette.
Speaking of reality and sports figures, I guess The Miz and Ronda Rousey fit the bill as celebrities turned wrestler, depending on what you consider a celebrity. I've always heard that while the Miz talked about wrestling throughout his Real World run, he was untrained when the episodes were shot. Likewise, Rousey was a huge name in the MMA world in it's hottest era in pop culture relevance, referenced wrestling constantly, but only started training when the WWE showed interest. Those two names are probably the closest to being real answers.