It appears no.
3rd Regiment, Georgia Cavalry
3rd Cavalry Regiment was organized by Colonel M. J. Crawford and mustered into Confederate service at Athens, Georgia, during the early summer of 1862. Some of the men were from Rabun, Whitfield, and Cherokee counties. It fought in Kentucky with General Wheeler, but at New Haven most of the unit was captured. . . .
https://www.nps.gov/civilwar/search-battle-units-detail.htm?battleunitcode=cga0003rc01