No.
Sporting Clays courses include presentations that are like Skeet and Trap, among other things. Sometimes the courses literally include a Skeet or Trap station, or Skrap, etc. People don't change guns to shoot them. The same shotgun breaks 'em all, or doesn't, depending on the shooter.
Trapshooters "need" special guns to shoot American Trap. But then, "trapshooter" is the equivalent of an ethnic slur among other shotgun sports enthusiasts. The consensus among essentiallly all the Skeet and especially Sporting Clays shooters that I've met is that they "need" special guns because trapshooters actually can't shoot too well. I've found it to be true of myself when I was a budding trapshooter: I used to shoot a lot of Trap, and I quit because I found that, when push came to shove, I couldn't shoot very well even if I shot Trap pretty decently. I started shooting Skeet and some Clays, and I studied up and took a lesson to help deprogram myself and re-learn some fundamentals, and I found myself shooting much better.
Now, I've gone back and shot a Continental Wobble Trap round a couple times for practice, and I hit 23 consistently with my Sporting Clays gun, after I'm already tired out, and regular American Trap is slower with far less variation in target presentation.
If you want to shoot Trap competitively every weekend, you might benefit from a specialized gun. But if you want to learn to shoot well all around, for hunting, Sporting Clays, just for fun, or even for less serious after-work leagues, one good gun THAT FITS YOU and that you like will serve you quite well.