I doubt they would. Assimilation was more the rule than the exception in the southern colonies.
You must be thinking of the later Federal expulsion of Cherokee that occurred. There were Cherokee units fighting for the Confederacy, you know. In fact, the last unit to lay down arms was Cherokee.
They were sorely abused with the Trail Of Tears, but southerners had next to nothing to do with it.
Andrew Jackson was a southerner, wasn't he? And he was the driving force behind the expulsion of the Cherokees - witness his famous statement about Marshall enforcing his decision regarding the Cherokees.
And the Cherokee unit in the Civil War was fighting in Indian territory, I believe, for their own perceived self-interest.
Righto, except for the southern slaveowning Tennessean president Jackson, who ignored a Supreme Court decision favoring the Cherokees. And, of course, for the Georgia state legislature and militia, which created the mess in the first place by unilaterally ignoring federal treaties.
You seriously think the impetus to expel the Cherokee and other southern tribes came from northerners, not the southern people who actually wanted their land?
BTW, Cherokees had their own civil war during ours. Units fought for both sides.