Gary,
I really don't know if that is the same William M. Haygood. There were at least two men from Georgia with the name William B. Haygood was from Watkinsville and I know that he was at the Wilderness battles. Family lore says that William M. came home following the 6 month enlistment in this particular Regiment. The papers indicate he had signed up for a 6 month period. He went back to the war (I haven't been able to find another enlistment) and was killed.
Thanks for all the help!