Yes, the Cherokees did unite behind the Confederacy, because they had no trust at all of the Federal government and a special animosity toward Andrew Jackson.
The only people of that region who did not get sent on the Trail of Tears were the Catawba, because they actually helped the Federal Government return slaves to their owners.
As an aside, they were consuming themselves in alcoholism and dying out in the last century until they adopted Mormonism and stopped drinking. They have a healthy little community now in South Carolina.
according to Dora Gray, by the time the war was over EVERY male over the age of 12 (who was physically ABLE to bear arms) had served in the CSA or tribal military forces.
fyi, NUMEROUS Tsalagiyi ladies had also served. (fwiw, Tsalagiyi women have always been FREE to be WARRIORS! there is even a WOMAN's WARRIOR SOCIETY. my niece can hardly wait to be old enough to join.)
free dixie,sw