She'd be stupid to compete on him.
There is the possibility that he just won't have the "want to" to run barrels, in which case he'd fail and she wouldn't be able to market him.
What she is selling isn't Clayton, she's selling Scamper. So she can't really let Clayton do anything . . . hell he might turn out to be an awesome calf horse which would ruin her marketing campaign.
She's doing the smartest thing by breeding him to mares that are proven and "select", which gives her a great chance of being able to sell him later based on his pregeny.
I agree that while he may have been a clone of Scamper's genetics, the environment that Scamper was nurtured (or not) in is what made him the horse he is. I really don't see him as being the same as Scamper when I look at him, I kinda see him as being close to a son or brother to Scamper that you can breed to. Like Tamet said, environment alters genetics and I too believe that the recipient mare had to have at least some effect on the embryo's development. So with that, I tend to think of it as similar to breeding to a son of Scamper.
And for someone like Skillz Schuman who doesn't breed solely on lineage, Clayton is not the way to go. But there are those of us who breed based solely on the name. I've seen a son of Frenchman's Guy breeding for like $1000 and he has never done anything. They don't list any earnings of progeny or the stallion himself. But folks are breeding to him just because he's a son of Frenchman's Guy. I would think that those folks will be the types to breed to Clayton.
And when they allow clones into the AQHA, and it's just a matter of time before they do, she'll be able to up his fee even more.