Well, while you seem to have some understanding of this from a high level, the repeaters have little to do with it. The linking happens at an IP level across the Internet, not RF site to RF site.
Tenn, does actually have some linked GMRS repeaters but not on the MyGMRS system. They run a private system that I know for sure exists in the Gatlinburg /Pigeon Forge area at least and extends into two neighboring states.
That being said, there is nothing restricting you from putting up your own repeater and linking it to the My GMRS system from where ever you land in Tenn. But, Tenn may NOT be considered a "MidWest" state and you may find out that the system fathers prefer you link to one of the eastern hubs and not 169. But that is not my call. Just a reminder before you go put a bunch of money down on a repeater system to find out you can't put it on MidWest. reason I bring that up is you specifically posted the linked "MidWest" repeaters on your attached photo.
I would discuss with the major players of the MidWest system Your intentions prior to committing to purchase of equipment.
I am trying to grow Ohio currently. I am actively hunting sites to install equipment on and look to put up at least two more repeaters in the central Ohio area myself this year. That being said, this is not an activity for those that are not well versed in radio communications equipment and the support of it.
I work as a commercial radio tech. GMRS and Ham radio are my hobbies. But I can speak from first hand experience that finding assistance for repeater site support and equipment repair and maintenance if you can't do it your self to run right around 100 to 150 dollars an hour for that service. That is going to be a pretty consistent number. If you find a tower site and are required to have professionals (most always the case) do the climbing and installation of an antenna system. That cost can easily run 4 to 6 thousand dollars for a single days work. And we haven't talked about the cost of antenna's, feed line, duplexers, a repeater or any of the other costs involved including a mandatory requirement for an Internet connection at the site for the actual link.
And the state to state, town to town communications that you see as being such a wonderful thing is only as good as the ISP level of service at your site and the site you are linked to. If either are down fro any reason, you will be down until the Internet service is restored.