Does not look like a clear match. I am inclined to believe however that there is some relationship, because of their locatation in Milledgeville, because of the surname GIBSON, but also because of the affluency. My GIBSON ancestors' appear to have been reading and writing in the 1880 and 1900 censuses. And George Sr.'s wife Louise CLEMMONS was a school teacher. She appears to have been raised with another family whose head "worked at a hospital."
Patience GIBSON was a slaveholder in Milledgeville. Have you done any research on her?