Yes. Barbecue sauce can and will burn if it's cooked, grilled or smoked for too long.
The sugar in the barbecue sauce caramelizes as it's heated, and if it’s left on heat for too long that sauce will burn and have a terrible taste. As a general rule to go by, the sweeter the sauce, the gentler you'll need to be with the heat and the time when you put it on.
So how do you avoid burning barbecue sauce? For starters, be gentle with it. Don't let your barbecue sauce remain on heat for more than 30 minutes. Remember, sauce should accent the flavor, the tenderness and the moisture of the meat. It's meant as a compliment.
The true star of barbecue is the flavor of the meat. When in doubt, glaze or baste your meat with sauce toward the very end of cooking, grilling or smoking process, or you can even sauce the meat just prior to serving.