That application is from the Sons of Confederate Veterans and would fall under a descendant organization.
Given your scenerio, I would be eligible because of my Confederate ancestors (plural) service in the Civil War through the Sons of Confederate Veterans (if I were still a current member) for recognition.
The United States Armed Forces does not give awards or recognition for a service member's ancestor's service.
Respectfully,
Gerald D. Hodge, Jr.
Lieutenant Colonel, U.S. Army