Definitely not! Cutting pizza with scissors/kitchen shears is far more effective. I'd never cut home-cooked pizza with a wheel if I had my way. Unfortunately it tends to upset Italians and other sticklers for tradition.

I can only imagine the cheese layer getting plaqued onto the shears.

I've used the sharp wheel thingy (didn't know it was called a pizza knife) in the past. It's nice but only good for that one purpose.

Kitchen shears are far better than a regular knife because they give you a lot more control, it's easy to cut different sized pieces. Plus, shears are useful for other things too (butterflying a chicken, for example).