Yes, they can, and do. However, they still need a large enough source of water to enable them to dunk their heads into it. They must clear their nares (nostrils).
My ducks seem to enjoy playing with the nipples more than using them for drinking. Matter of fact, they've managed to remove one of the metal "click it" valves from one and emptied the entire bucket of water.
I was just about to ask this same exact questions. I've got chickens down pact & this winter (if you want to call it that lol) I have been converting a pen to hold them. I was wondering if their beaks could push in the ball. Anyways... BYC to the rescue!