Having reviewed literally thousands of service files of officers and men who enrolled in the 1st Alabama Regiment, I cannot imagine that this John McCluskey has any connection with your ancestor from Calhoun County. Barbour County is quite some distance away, and if your ancestor was inclined to volunteer, other companies were being recruited at White Plains. For instance, Samuel A. Morgan, who lived in the next household on the census after John McCluskey, enrolled in the "White Plains Rangers", Co. "C", 5th Alabama Battalion. Based on his age (37 in 1861), having a wife, three small children and a farm to care for, most men in Alabama in a similar situation would not volunteer. Most men that I checked who volunteered for service in the 1st Alabama Regiment were younger and single and did not own a farm.
Several men named John McCluskey or McClesky are living in Alabama in 1860. Does your ancestor have a middle initial? I could not locate him on the 1880 census of Denton County TX.