From everything I've ever heard or read about Kaman, it sounds like his character is beyond reproach. As for how he'd fit with the current team, I don't think he's any slower or less athletic than Roy or Rasho, so I think he'd fit in just fine.
What I really like about Kaman is that he's a true beast on the boards. Right now, I don't really think you can play Danny at PF for extended minutes because our rebounding suffers. If you have Kaman in the middle, you can move Danny up to PF almost anytime they're on the floor together.
I'm very happy with the current roster, but I think you'd really have to listen to offers like Kaman for Dunleavy, Rasho and Hibbert, or 'Quis and Hibbert.