I believe they do, even though most graves are unmarked. There are some in-ground headstones for some individuals buried there, but they look modern, as if modern family members knew their ancestor was buried there, so they secured a headstone. I doubt if the headstones in place reflect the known location of the ancestor's grave. The office at the main entrance is open 9:00 am to 5:00 pm, and you can ask if they have a list. BG John Echols and MAJ Jedediah Hotchkiss are buried at Thornrose.
Here is the cemetery's web page.
http://www.thornrose.org/home.html

Contact Thornrose Cemetery by mail at:
Thornrose Cemetery
1041 W. Beverley St.
Staunton, Va. 24401

By telephone at:
540-886-8241