Well I guess it would be best to compare the date of the land patent and the date that Abraham owned the Franklin plantation. Im not sure what the odds of him owning land in AL and GA are( if he was wealthy than it's possible). As an Aderhold and after researching the name just a bit, it is my experience that the Aderhold name was not that dense in the population in that time era and more than likely AL Abraham was also GA Abraham. I am no expert but I say it is a good chance that they are the same person.
I am currently on the trail of my immigrant ancestors. Apparently each of the Aderhold branches (Aderhold, Aderholt, Aderholdt) all came from Jacob Aderholdt who came from Germany in the late 1600's. This stuff is fascinating to me, if I come across anymore Abraham's in my search I will let you know!!!