I have no satisfiablility built in: no level rating, no guarantee of uniqueness. It just makes sure the game constraints and the parameters passed are met. That being said, building satisfiability into would be a nice challenge. I would just need some ways to measure difficulty, etc.
Nice job on the generator, it take a lot of work to get right. Anyway, no code, but here is a good Kakuro game with uniqueness, different levels: http://www.atksolutions.com/games/kakuro.html