The legs are definitely used to pitch and there is a push against the rubber. You want your stride to be as long as possible while still being able to maintain good posture and balance and getting good hip and shoulder rotation. To do this, you need to get your hips going and that requires a push with the throwing leg against the rubber. But, to me, it's more of a subconscious push. I never tell my pitchers to "push off more" or anything like that - I only talk about their knee lift and getting their hips going.
Often, when a pitcher tries to intentionally push off the rubber, they mess up their timing.
BYW, most of your velocity is generated by the rotation of hips and shoulders - not movement down the hill.