No, you understood it correctly, though it's not specifically/only used with one group of people or another. The idea as you said is to lay low, to pretend to be weak and helpless مسكين, until one's able to reach power.I thought the idea was to lay low until you get the upper hand when circumstances change in your favour. Did I completely misunderstand it?
دخل على المدير بالبيضة و الحجرI don’t know what دخل على المدير بالبيضة والحج means. For the rest, maybe:
He wallowed in affected self-pity he got more power/clout, and now he all but runs the team.