The word adoption like reservation is a white man's word. This is a term and concept unfamiliar to the Cherokees.
The only time I've seen that term used is on the Dawes Roll. Whites who were married to Cherokee spouses were Cherokee by Intermarriage and the Dawes Commission considered them *adopted* apparently because that term was then stamped on the enrollment card.
These white terms apparently conferred on them the right to obtain land allotments in their own name prior to about 1870, after 1870 the Commissioner decided intermarried could not obtain land allotments in their own names.
Whites intermarried with Cherokees were "accepted" so to speak but it is only in the white literature you will find any terms like adoption or that whites not intermarried were *adopted* by Indians.