I'm going to the periodonist today to get surgery done. They are going to take skin from the back of my throat and use it as my gums. Does that sound normal?

Almost. I think you misunderstood. This tissue is harvested from the palate and then sutured where it is needed. The back of the throat would be a hard place to reach and the wrong tissue.
Free gingival graft. Free gingival graft is one of the method to extend the attached gingiva, which in many situations, served as protective function in periodontal health. I am not sure he is using free gingival graft or connective tissue graft. Nevertheless, the tissue taken usually on the palate in front of the molar area. Trust your periodontist since he is trained in this area of grafting.
Gum grafting. I have never heard of taking tissue from throat for gum grafting. Usually the tissue is taken from the roof of the mouth. That is more the standard way to do this. I think if you ask to see exactly where they will be working, you will find this to be the place. Good luck with everything.