Originally Posted by Rick DeBay

I don't even think a large number of these missiles could give you a mission kill (mission being defined as aimed firing of the main armament). You could sure as hell perforate the superstructure pretty well, and even blow the bow off. But it was designed for such occurrences (it'd cruise REALLY SLOW though :-)

Seriously, unless the warhead is designed to penetrate armor, it'll break up on impact with the main armor belt, and maybe even with the hull (which is twice as thick as current armor, don't Burke's have 3/4 inch hull plating?). Even the dreaded Moskit in a plunge from altitude wouldn't have enough of a punch even if it's semi-armor piercing warhead was replaced with a hardened one.

Best bet would be a missile with a BIG shaped charge. An AS-4 Kitchen would certainly be enough, Russia claims it'll put a 5 meter hole 12 meters deep in any target.
Anything smaller that survived to impact on the armored belt would have to cross an eight foot void behind the belt before there was anything to damage. You'd have better luck hitting the armor deck, there's much less of a void between it and vulnerable machinery. You wouldn't let any water in (which leads to sinking) but you'd start fires which might eventually put it out of action.