What a hilarious concept! We could even ship them some lions and lambs so they can try to make them get along.
Here's what I think would happen. When they first get there, they'd be elated, they'd think they had finally found real paradise. Of course they would immediately implement their "high control" structure, and with no door-to-door work to do, they could spend extra time at the KH. If the island was small enough to get around on foot, there would be no industry, just a mindless slave class farming, praying, and serving their theocratic overlords. With no printing presses, the brainwashing would have to be word-of-mouth.
But eventually reality would creep in. Human nature would creep in. There would be power struggles, especially in the GB. One of them would eventually figure out the real truth, that might makes right. That person would kill the rest of the governing body and seize control, then rule with an iron fist.
Then the religion would erode somewhat. With actual physical control of the island, the new king wouldn't have to rely so much on the brainwashing to control the slaves. When they stepped out of line he could just hit them. The religion would still be there though, to reduce the frequency with which the king has to hit people, because he's getting old and his arm gets tired. However, with no outside world to contend with, the religion would no longer have to change.
Eventually the slaves would become irate and there would be a civil war, albeit a real sissy one.