After talking to the good folks at the Troup County Archives, we are about 98% convinced that Mary E. Mooty did not serve with the Nancy Hart's.
Posts on this board from the census and from the archives note that Mary and William were married in 1860. There was at least on child born during the time the Nancy Hart's were in service. Also Mary lived outside LaGrange, on the Mooty family property , her burial spot is on this same property. They found a newspaper that contained her obituary, which was very interesting. And I am finding out more about how she might have gotten a Confederate headstone, when I get some more information on this I will post what I find.