I would be cautious, since Thomas Edward King likely was not on Smith's staff at that point in 1862. King was actually the cousin of Quintard's wife, as they were both the grandchildren of early Georgia industrialist Roswell King, founder of Roswell, Georgia. Quintard dedicated his famous little book for wounded soldiers, Balm for the Weary and Wounded, to King. Note this from the dedication:

"This little manual is inscribed to the memory of Captain THOMAS EDWARD KING, of Roswell, Georgia, who fell at the Battle of Chickamauga, on Saturday, the 19th day of September, A.D. 1863.

His life was rendered illustrious by an exhibition of all those virtues which adorn the patriot and the Christian.

He was brave without temerity, generous without prodigality, noble without pride, and virtuous without severity.

Wounded at the Battle of Manassas, on the 21st of July, 1861, he was unable to resume the command of his company; but when his native state was threatened he felt that he must "join the struggle to drive the invader from his altar and his home." He accepted a position on the staff of the gallant General Preston Smith, and fell with him, at the close of the day, cheerfully offering up his life for his country's cause."

Note Quintard says King joined Smith when his home state (Georgia) was threatened, which suggests he joined in the summer of 1863, and if that was the case, he would not have been in Kentucky. Most certain way to see is to look at King's Compiled Service Record.