Well, according to my own research, some regiments did!
Sources:
-
The Illustrated Directory of Uniforms, Weapons and Equipment of the Civil War by David Miller
North Carolina Infantry private
Some wore epaulettes too, and even 1812 styled uniforms
Artillery too
Cavalry, as well, it seems
And for Union styled shoulder boards I've found a few resources, also from the same book
5th Georgian Infantry, Clinch Rifles
The Confederate Navy used Union-styled shoulder boards for its officers, too
Commander & First Lt;; WARNING VERY LARGE PICTURE
And the last, but not least
Admiral Franklin Buchanan, Confederate States Navy
Maybe I should have put adf.ly to get some moneyz, but naah, feel free to see and download, all are from the source stated above, scanned by me