I read it that way at first too, and while there might be a thread of truth in that theory I think it's also likely that he left it in Matt's apartment to guilt trip him. He probably did leave because of a mix of both (shit, he's getting attached, shit, I'M getting attached, this isn't good) but he also knew that Matt wouldn't fall off his radar completely. He knew he'd be going back to him some day, and Stick strikes me as the kind of person who wouldn't leave anything to chance. So he kept the bracelet as a reminder to himself that attachments are dangerous, and as a tool to use to control Matt later on.

Let's be real here, Stick has probably been right where Matt is with the whole abandonment issues thing, but he's hand longer to cope with it. It just happens that his way of coping is to be a complete dickwad to everyone around him. Matt is on that path, tbh, considering how hostile he can be at first to people he doesn't know, and even with how emotionally detached he appears even to his friends.