I mean, all five of the Five Civilized Tribes are Mississippian descendants; the Chickasaw simply happen to be the only ones we can connect directly to a specific mound site. But even the Cherokee were clearly part of the SEC originally.
The question is who would lead them? The most obvious option, John Ross, has the problem of being much like President Grant: a good guy presiding over an incredibly corrupt administration. Attakullakulla might work, but he's not exactly well known. His son, Dragging Canoe, is more famous but was also only a local warchief. The leader question has always been the biggest problem in my mind for both the Cherokee and the Creek.
I wouldn't even say it's a joke. To paraphrase one Native American scholar, half the white population of the US believes itself to be part Cherokee, a tribe they nebulously place anywhere from Maine to Montana.
A certain US senator springs to mind.
Possibly, but I foresee potential difficulties in either of those directions. They've already been rebuffed by both the Haida (presumably) and the Tewa, and other tribes in the area may feel similarly or Firaxis may be hesitant to try again. At which rate a Plateau or Plains tribe might be Firaxis' next choice for "out West," but I'm not particularly eager for another nomadic horse raiding civ personally.