Of course it does, and nobody expressed it better than George Orwell, who wrote, "All the animals in the farm are equal, but some are more equal than others."
Does equality exsist?
Only on paper
I would say it does not. The system that we are in is setup on greed and selfishness. It perfectly reflects it's ruler. The bible says at 1John 5:19 "The whole world is lying in the power of the wicked one". Until rulership of the world has been resolved we will not see true justice and equality. The bible also says that it is God's purpose to accomplish this very thing and He will not be relying on the cooperation of man to do it. The scriptures also say at Rev 21:3,4
"With that I heard a loud voice from the throne say: “Look! The tent of God is with mankind, and he will reside with them, and they will be his people. And God himself will be with them. And he will wipe out every tear from their eyes, and death will be no more, neither will mourning nor outcry not pain be anymore. The former things have passed away."