The original company letter designation ("I") and WCC's date of enlistment answer your question in the affirmative. Clouse entered service as 4th Sergeant of Capt Gordon's company. Organizing at Long Island, Jackson County, Alabama, Apr 15, 1861, Capt John B Gordon’s command entered state service on Apr 25, 1861. Members arrived at Montgomery on May 7, 1861, and mustered in Confederate service May 15, 1861. The company reorganized as 2nd Co “D” on Apr 28, 1862.
Clouse's service file includes a petition for an articial limb.
Here's Gordon's account of the company's attempt to enter service. Note their petition to a state governor and not a representative of the Confederate government, with acceptance hardly being automatic. People seem to overlook these important aspects of volunteer enlistments during 1861.