Do remember that sewing machines sewed only straight stitch in those days. A number of details still needed to be done by hand, especially seam finishes, buttons and buttonholes, gathering, and various tailoring details (I'm not that familiar with tailoring). However, I suspect that the only uniforms made entirely by hand would be officers' custom tailored uniforms (tailors seemed rather resistant to using machines). If your reenactor is an officer, he would be correct. If he's an enlisted man, probably not.
I learned to sew on a treadle machine, too! After yet another recent session resulting in very unladylike language about my modern machine, I wish I still had that old one!
I found references to treadle sewing machines during the Civil War in James C. Mohr, ed. The Cormany Diaries. University of Pittsburgh Press, 1982. Rachel Cormany's husband bought her one after he went off to war, so she could earn some money (difficult because her husband's family all seemed to think she should make their clothes for free). This was in, I believe, 1862.