South China Sea is as important to China as the Caribbean is to the United States, or the Mediterranean to Europe and Africa. The ADIZ mechanism is not all that unusual. The United States, Canada, Japan, and South Korea each maintain an ADIZ.
I suspect China will have to in order to further discourage the United States from conducting surveillance flights near the submarine base in Hainan. It is more likely China will announce a smaller ADIZ that it can enforce with fighter jets, but even this will antagonize Philippines and Vietnam, at a minimum.
China announced their ADIZ in East China Sea unilaterally, without consulting with the United States or Japan. The question is whether China will consult with United States or neighboring countries.