You have identified a different man.
On Apr. 29, 1861, William T. Bennett enrolled in Capt. John Bunyan Taylor's Co. "F", 4th Louisiana Regiment (later Co. "I"). Bennett's military service file shows that he was wounded at Shiloh and Baton Rouge, and thought to have been killed in the Battle of Jonesboro GA, Aug. 31, 1864. Bennett was captured and sent to prison camp at Camp Douglas in Chicago IL, suviving to be exchanged At Boulware's Wharf on the James River in Virginia on March 21, 1865. He was sent home and still on furlough when the war ended. Here's a regimental history.
http://www.4thla.org/HISTORY_4THLA.htm
Copies of Bennett's military service file are available here --