This has been happening for over a century at least, although not as dramatically as either of the scenarios listed. It's not a "sudden takeover" deal, and it's usually not an entire county, but there are small towns and areas of the United States that are controlled by insular cults. They choose remote locations that allow the cult leaders to control the flow of information. Also, the local police are all members of the cult -- a lot of the time they're more like a private death squad, and they're basically useless in combating the cult's illegal activities. Dissenters get kicked out and possibly killed.

The Fundamentalist Church of Jesus Christ of Latter-Day Saints is the best-known example, at least around here. There are documentaries and interviews if you're interested in learning more about this stuff. It's extremely depressing, but worth learning about if you're curious.

To actually answer your question, I don't think a sudden takeover would last very long. It would probably just be a longer, bloodier version of the Ammon Bundy fiasco in Oregon. Like others said, they people in charge would more likely just buy the land outright.