There are very few MLB pitchers who actually are examples of "drop 'n drive". Most do what bamajeff noted. They simply think of moving their front hip out. Yeah, there's a push there. There's no point in arguing it's existence. It's just not a "drop 'n drive". Nor is it a "tall 'n fall". Both of those are too limiting to describe complex full body motions like pitching. The push/no push argument is a waste of time and effort. Been there, many times with both sides. How do you define "push"? When do you do it? To what end?
A good term I heard once is "rotational push". I kind of like that term. The lesson here is that it is fruitless to think of pushing off the rubber. It CAN (not "will") lead to problems with timing and getting the upper body moving ahead too early. It CAN (not "will) lead to the hips opening too early. The most productive thought on it is to simply move the front hip and the centre of gravity out first and hard. Then think of the rotational push idea. Just rotate the core hard into landing, assisted by the back foot and leg rotating and extending. It's the rotation that's important here after a good sideways motion out with the front hip.