Yes he does. He also does whatever he can to stir up controversy within the church - especially directing people to believe their brand of Christianity is better than any other (what we might call Phariseeism).
OTOH, Satan also serves the will of G-d.
Shalom.
You are correct. But the most serious problems problems in the professing Church are not the controversies between saved people, but the problems which completely lost folks pose within the professing Church.
And Satan does like to play shell games as to the matter of which folks are saved and which folks are lost. When someone with discernment uses the Scriptures themselves to clarify matters, Satan will ordinarily accuse that Christian of being a Pharisee. And he will use the real Pharisees in the case to make the accusation.
This is why Sola Scriptura is so important. We have to stand exclusively on what God clearly hath said. It's the only way out of the mess of Satan's lies.
I recommend that you check out Posts #33 and #53 on http://www.freerepublic.com/focus/religion/704064/posts to see what I mean.
And as I said earlier, Tim Rice, who wrote JCSS, is just plain lost. He is the enemy of God. This is not even arguable. But you have managed to overlook it. If you would follow Sola Scriptura, you wouldn't even need to read Tim Rice's confession that he doesn't believe the gospel. You would see it in his "rock opera."