Henry - What I am finding does not match with the information you provided. May I ask your source? There are records for only two men named Teague in the 19th Alabama. One is Warren H Teague, age 18, who was enlisted by Captain Jackson Millsaps, on Aug 14, 1861, at Broomtown. Capt. Millsaps' company would proceed to Huntsville where it was organized as Company G of the 19th. Private Teague was discharged at Huntsville on account of disability on the 29th of September, 1861. His discharge was signed by Col. Joseph Wheeler, Cmdg. 19th Ala.
The other man, according to family trees that I have found, was Warren Teague's father, Magnes (or Magness) Teague who was born about 1819. There is only one card in his file, showing that he enlisted in Captain Millsaps' Cherokee Mountaineers on July 6, 1861. Since there are no further records for this man, my assumption would be that he was discharged on account of his age.
The first reference I find to Henry Crawford Teague is to the man married to Cumie Speer. However, these people were not alive during the war, Henry being born in 1881, and Cumie in 1887. Henry's death certificate in 1939, indicated that his father was Warren Teague.
Any additional light that you can shine on these folks would be helpful.