Yes. The squabbling will increase until a new leader comes out on top.
I had to remove the top tier of my chicken hierarchy due to behavioral problems. Once the leaders were removed the fighting got pretty intense for about 2 weeks until a new bird established herself as leader. Funny enough, it was not the bird I had predicted would become top bird. A previously lowest ranking bird came out on top and cowed everyone. I'm OK with the results of the new pecking order. The newest leader is much more benevolent than the previous leader, and the flock seems more stable than ever.
Good luck.