I'd say no, Veidt doesn't have super powers. Giving him super powers takes away from one of the most important points in the books, that people in costumes in the real world would never have super human abilities, and if they did it would be frightening.
This is true, thematically. I'm not really disputing any of the book's central themes of power and I'm not trying to subvert the expert deconstruction of the superhero genre and its tropes.
I guess one thing I would say is that, even though Watchmen deals with character and conflict in a realistic way with realistic dialogue, it is in no way a representation of a realistic world. Yes, it feels more "real" because of the human three-dimensionality given to the characters, but a world full of genetically-altered lynxes and flying owlships is no more "realistic" than a world of radioactive spiders and Batmobiles.
Even the fact that there's only one superpowered being that we can confirm in Watchmen, that doesn't mean that there aren't others. For the sake of the story and the themes, Dr. Manhattan is the only one that matters. My point was that, perhaps Adrian, or psychic Robert Deschaines, possess abilities that are superhuman in nature. Maybe Adrian's mastery of his brain and body were evidence of other people who possessed abilities besides Dr. Manhattan.