Chuck, LOTS of physicians served in non-medical positions, both as officers and in the ranks. To illustrate, I did a search in my Arkansas soldier database under surnames beginning with "S", and just the first few hits found these --
Moses M. Sanders, 1st Arkansas Infantry.
Thomas J. Scott, 1st Arkansas Infantry.
Joseph E. Seymore, 6th Arkansas Cavalry.
Frederick L. Sherrer, 2nd Arkansas Cavalry.
John G. Simmons, 26th Arkansas Infantry.
Hamilton P. Smead, 19th Arkansas Infantry.
James T. Smith, 2nd Arkansas Mounted Rifles.
Stephen Smith, Etter’s Arkansas Battery.
Then I terminated the search, because I think the point is made. These men could have applied for an exemption from service, but elected to remain in the ranks. No wonder there was a shortage of doctors back home. Interesting, huh?