You can't be serious. There is ZERO chance. You'd have a better chance bringing down a 747 with a BB gun a mile or two away from an airport than they would have hitting the POS shuttle.
Well, I said I was completely clueless about both missiles and shuttles.....but the reply above from AmericaninTokyo makes sense that they would still do it just as a PR stunt.
However, what they CAN do is time a transpacific launch of a Taepodong-2 at the same time the Shuttle returns, for PR effect--the same day, same hour, what not.