Your William Braden is a different man than the one who enlisted in the "Franklin Blues", Co E, 2nd Alabama Regt., and later Co A, 27th Alabama Regt. That William Braden appears in the 1860 census in the household of Andrew Braden, eastern Franklin County AL.
The other William Braden lived in St. Clair County AL and served in the 10th Alabama Regt. We've already reviewed that solider.
The only Confederate service file for your Willliam Braden appears under the name, William M Bradon, Co E, 2nd Mississippi Regt, enlisted Guntown MS, Mar 3, 1862, age 31. The record states, "entry cancelled", so it appears he did not actually enter service with this company. That's the only record for this man.
Mississippi records show that he married Elizabeth Holiday on Dec 17, 1857, Itawamba County MS.