Two additional bits, for what they're worth:
New York Times, 30 November 1862:
GEN. BUTLER'S ORDERS.
HEADQUARTERS DEPARTMENT OF THE GULF,
NEW-ORLEANS, Nov. 18, 1862.
[This section specifies the order of inspection for the following units: 26th Massachussetts Volunteer Infantry, 30th Massachusetts Volunteer Infantry, 9th Connecticut Volunteer Infantry, 2nd Massachusetts Light Artillery Battery, and "The Three Batteries of Regulars, under the command of Capt. DURYEA, U.S.A."]
VI. This inspection is intended to be thorough and complete. The troops will be formed promptly at the hour designated, on their usual parade grounds, in full marching order, with knapsacks properly packed, containing great coat and blanket. All clothing belonging to the soldier must be either in his knapsack or upon his person.
By order of Maj.-Gen. B. F. BUTLER.
N. A. M. DUDLEY, Col. and Act. Inspector-General.
New York Times, 12 August 1863:
[Letter from correspondent "C. L. B." bylined "WINCHESTER, TENN., Tuesday, Aug. 4., 1863. Letter goes into extensive detail about camp conditions in that part of Rosecrans' army he was visiting:
Soldier's camps in Summer are by no means romantic or interesting things; villages of arbors, covered with brown branches, dirty, hot and sweltering, with tin cups, newspapers, blankets and equipments lying about in confusion; long lines of mules and horses, kicking and fly-bitten, the men sauntering under trees or about the stations in flannel shirts and trowsers. Every one who could was reading newspapers, and all were orderly and well-behaved.***Nothing will ever give us rapid marches and efficient movements but a reduction of transportation. The men in this climate have already abandoned their knapsacks. The officers ought to be equally cut down in their comforts and luxuries.
NOTE: I don't want to draw too much from the above items, but these suggest two things:
1. Greatcoats, when carried, may well have been placed inside knapsacks rather than strapped to the top, assuming there was enough room.
2. In the case of the second letter, which indicates many, if not all, troops didn't even have knapsacks on which to strap greatcoats (assuming they were still in their possession anyway), your question is interesting but, depending on the scenario, may well be irrelevant.