I don't know for sure, but I'm gonna say highly unlikely.
I've don't recall seeing any M1841, or "old pattern" great coats in any inventory of 1861 Southern captured depots I've read up on, and I'd bet there were none in the North as they were making then current M1851 pattern in gray, and black from contractors as there was a shortage of greatcoats and sky-blue kersey. If they had a shortage, they were running low on the current issue, and in the mid-1800's that meant they didn't have the old pattern.
The sky-blue CW pattern was adopted in 1851, and that's a long time to expect old patterns kept on hand. Especially in an era where the Army kept everything and used the stocks of it up till it was gone before adopting a new one. So extremely unlikely.