Note that the 2nd Regiment, Cherokee Mtd Volunteers (Adair's) did not officially exist until Feb. 3, 1863. Prior to that, what became company F was attached to the 1st Cherokee Mtd Vols (Watie's), designated co. M under Capt OHP Brewer (an ancestor of mine, btw). The core of the 2nd Regt was the five companies of Bryan's Battalion. I don't find a record of Noah Scott with the 1st Cherokee Mtd Vols though there are a number of Scotts in that regiment. I didn't find a Noah in the Old Settlers Roll (1851), the Drennen Roll (1852) or in Starr's "Old Cherokee Families" though there are many with the Scott surname.
On April 1, 1863, he was on extra duty for the Quartermasters Dept.
Others who enlisted in Co. F, 2nd Cherokee Mtd Vols, Oct 12, 1862 at Ft Davis.
Benge, Samuel
Colbert, William C.
Hanks, R.T.
Looney, William
Reynolds, Anderson
Sturtevant, M.B. (formerly 1st Cher Mtd Vols, co. G 1st org.)
This group is curious since they are the only persons in the regiment enrolled in October, all on the same date into the same company. Most members of the regiment were enrolled ("re-enrolled") July 12th, the end of their original one year enlistment. The additional companies of the 1st Regt that were added to the 2nd Regt were created on or after July 12th.
I'm fairly certain, without more research, that Benge and Looney are Cherokee. Cobert may be Cherokee though that is a very common Choctaw/Chickasaw surname. There were many in the two Confederate Cherokee regiments who were not Cherokee citizens, predominately from Arkansas but also Missouri and elsewhere.