Yea, one one reason Zakk can do harmonics so distinctivly is because of his pickups. The pickups are the main factor in his sound, and not so much the guitar. He also has a tendency of ramming his flesh into the strings with his picking hand while doing harmonics. (extreme harmonics, it wouldnt squeal on your or mine guitar, because the pickups arent disigned to. It would just make the note dampen).

Also, its not only how he does harmonics that makes him sqeal, its how he bends.
Most people, when bending do this:
E------15b17~~~~ and they vibrato on the bent note

Zakk does:
E------15b17r15b17r15b17~~~~ which takes alot of finger strenght because he does those bends in a very fast rotary way of using his wrist to bend instead of his fingers.

Also, this kind of bend would sound just AWEFULL if done alone, it has to be harmonized properly to give it that head ripping feel.