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The game 'Rome II: Total War' suggests they could be employed in a Phalanx, and have long pikes while maintaining 'Egyptian-looking' armour. I'm guessing this has obvious historical failings though...
Paradox generally does a good job on their history, for a video game, and I'd be surprised if they made an elementary mistake. Whoops, Total War is by Creative Assembly. Don't know their rep for historical accuracy.
The basic phalanx, soldiers in a tight, rectangular formation moving forward as a unit, usually with polearm and shield, was around for millennia by the late Egyptian period. The earliest depiction is in the Stele of the Vultures celebrating a victory of Lagash over its neighbor Umma around 2500 BC.
It remained, with many tweaks, the dominant form of warfare in Europe and the Near East until the Roman army of the middle republic developed the more flexible legions around 250 BC.
After Alexander The Great conquered Egypt in 332 BC, their armies followed the Greek model and their main military force moved away from bowmen and chariots to heavy infantry. After that point yes, Egyptian infantry would definitely be in a phalanx formation, wearing armor, and wielding pikes.