Yes, but we are talking about "clam Bake" and not Viva Las Vegas,
Elvis raced a boat and had the car as a sportscar, he was a rich guy that switched roles with his mechanic so he could get a girl to like him for who he was and not his oil money.
Took place in Miami and raced boats at miami marine stadium.
It could be the SR but I have seen it in person and this car is burgandy in the movie,
Although this film is set in Miami, Elvis Presley's scenes were all shot in and around Los Angeles. All the Florida exteriors were shot in wide angles, using doubles for Presley.
Elvis' red sports car in the film is a 1959 Chevrolet Corvette Stingray Racer.
This pic show the car off better, and it is the sting ray racer:
this article refers to the Petersen museum and GM heritage collection and calls the car the SR3
A 1959 Chevrolet Corvette Stingray 3 concept car appeared in "Clambake," a 1967 movie starring Elvis Presley and Shelley Fabares.