Should chicken be cooked beforehand while making pizza?
Cook the chicken ahead of time. I doubt your pizza cooking time and your chicken cooking time will be a perfect match, and it is more likely than anything that your chicken would be undercooked. That would not be good for anyone.

If you are worried about the chicken being dry on your pizza, you can try par-cooking the pieces instead of fully cooking them (though that may be a little dangerous, too), or you can add the cooked pieces to the pizza after it has begun baking.