Good question.

I don't think the hellenistic phalanx has such a strong push. I mean it doesn't seem possible and useful. If they hold their pikes 2handed and the backrows would push the ranks with the sarissa lowered can't use their pikes anymore. a spacing between the ranks is needed so they can use their pikes. so no pushing from the rear i guess.

The classic phalanx was all about the push and its main instrument the shield, the spears being only secondary. There you push forward with the shield against the back of the guy in front of you until the enemy line breakes.the chance to inflict bigger damage with the spear is very limited.at least that's how it works in phalanx vs phalanx. against the persians for example they fought slightly different (see Kunaxa for example).

The main instrument of the pike phalanx is the pike to keep the enemy at distance.

They are 2 completely different things imho although having the same roots.