The theory is the closest to being sound that I have heard, but I doubt it would work. A 10mi x 10mi wide region is only a very small fraction of a hurricane and would likely have a negligible effect. Cold water is denser than warm water, I do believe, so the colder water is going to tend to sink back down to the surface. If it didn't, you risk affecting/damaging the ecosystem of the ocean there -- certain plants and fish depend on particular temperatures of water -- unless you had some way of reversing it on its own.

But, at the very least, it's better than the other ideas I've heard. Dynagel...argh. And the idea of dropping water-absorbent material from the air into the storm itself -- well, that cuts off evaporative cooling due to precipitation, which may well lead to warming inside the storm enhancing the warm core; at the very least, it certainly won't cause the shear it's inventor wanted to creare. Don't want to enhance the storm...