There was, in fact, a single known Armenian to have taken part in the American Civil War. His name was Khatchadour P. Garabedian, a Lowell mill worker who went by the name Menas Garabed. From documents from the Lowell Mill we know that he had been discharged as a sailor from Philadelphia. He was a cabinet worker in 1855 according to a newspaper advertisement found, having lived to 1881 when he died. There was no stone marker at his burial site, however. A fundraiser was organized to make sure that the memory of this man is restored for generations yet to come, through a lovely gravestone.
More info: http://www.armenianweekly.com/2013/01/23/chance-discovery-leads-to-rare-armenian-hero/