Patti, when looking at Michael McGrath's record:

McGrath, Michael, Pvt. Co. C, K, 13th La. Inf. En. Sept. 11, 1861, Camp Moore, La. Rolls June,
1862, to Oct., 1862. Present. Roll Nov. and Dec., 1862, Absent, sick. Rolls Jan., 1863, to Oct.,
1863, Present. Rolls Nov., 1863, to Feb. 28, 1865, Absent, missing, since battle of Missionary
Ridge, Nov. 25, 1863. Federal Rolls of Prisoners of War, Captured Missionary Ridge, Nov. 25,
1863. Forwd. to Military Prison, Louisville, Ky., from Nashville, Tenn., Dec. 6, 1863, Transfd.
to Rock Island Barracks, Ill., Dec. 9, 1863. En. in U. S. Navy. Transfd. to Naval Rendezvous,
Camp Douglas, Ill.

Looks like our guy was captured on November 25, 1863 at Missionary Ridge and joined the U.S. navy...doesnt sound like he was sent out west. Dont feel bad, lots of the New Orleans boys from the 13th and 20th liked taking the oath and joining the U.S. army. :)