You CAN push off damage, but I wouldn't suggest it when both teams have the same numbers. Sure pushing off good damage is an advantage for you, but you are pushing into a defended position which gives the other team an advantage, plus they have sticks up somewhere which you need to deal with so that's another advantage for them. If you have über advantage or more players up you could push on good damage, but in those situations you already have a big advantage and would be pushing anyway.
You don't need to sit around all day waiting for a pick to push, but It's the smart play IMO