Dear Mr. Lee,
Many of the 36th Georgia soldiers were captured at Baker's Creek (a.k.a. Champion's Hill) on 16 May 1863 along with soldiers of the 39th Georgia. During the capitulation of the Vicksburg garrison, these soldiers were going through the prisoner of war system in the north. Many of them by this point in time were being exchanged at City Point, Virginia. Their names would not have been on any list if they were not physically present at Vicksburg. The Federals were pretty meticulous from what my research has found.
I hope this helps.
Respectfully,
Gerald D. Hodge, Jr.
Niota, Tennessee
War Between the States Historian
Historian: 39th Georgia Infantry Regiment
Web Master: http://39thGAVOLINFRGT.homestead.com/39thHomepage.html