Hopefully, they won't shut down, but having Plan B is a good idea.
Since you will be a couple weeks ahead of the colors, getting other sites last minute should not be an issue.
As mention, GA state parks in the mountains would be a good backup. In the GA/TN area is Cherokee NF. You can dispersed camp along gravel roads as long as you are 300' from the paved road and not blocking traffic. Since this does not allow upons services, you will still be able to do this.
There are also numerous commercial campgrounds which would not be bad option for backup plans.
