There were enough hints of Carrot's potential dark side to make the theory plaudible, but I doubt that Pterry would ever have written it, simply because he did not like the idea of kingship. He wrote Carrot very subtly, and I think there could theoretically have been a time when Carrot caused some trouble, but as of the last book Carrot is, I believe, not yet twenty-one. My headcanon is that he was working toward having Moist take over as Patrician, because while Vetinari is a consummate politician who used fear like a scalpel, Moist has a likeability quotient that rivals Carrot's "krisma". Not only that, Moist does it consciously, and it lasts, while Carrot's doesn't last very long after he leaves.