Just off the top of my head, and believe me this is only an itial though, I don't think it owuld be a good idea. Although the string as a whole vibrates there are loads of overtones which are where parts of the string vibrate around various nodes down the string length. If the string is thicker between two of the nodes, it will (try to) vibrate at a different frequency to the section of the string next to it. If this is the case, I could see one dampening the other and making the overtones diminished.
But saying that, it could be the best guitar invention yet, you just never know