The below-referenced article on macadam road construction indicates that the first macadam road in the United States was the Boonesborough Turnpike Road, 10 miles long, completed in 1823. The second one was the Cumberland Road, 73 miles long, which was completed in 1830 after five years of work.
Of course, there were three decades between the completion of the Cumberland Road and the start of the Civil War, and more efficient techniques could have been developed during that time. Still, if it took a year to build 14 or 15 miles of one road in 1830, I'm skeptical that a network of macadam roads sufficiently extensive to make a significant difference in a war effort could have been constructed in the time available to the Confederacy.