It's frequently stated in the Georgia media that the Georgia voter verification uses the drivers' license database. Both the writer of the newspaper article I linked, and rpranesh (post above) stated that in order to update one's citizenship status in that database, one has to get a new license. (I'm guessing the DDS, or its software, has no other mechanism for changing this information).
On the US Citizenship forum, a few months back, I recall posts scoffing at the idea that one would need to make any kind of driver's license update after becoming a USC. That's probably the case in most states, but it's looking to me as if in Georgia, you have to go visit the DDS and they'll probably say you have to get a new license. If you don't do that, your vote will likely be challenged.
I'm speculating, though, that some of this may depend on how long you've had the license. I got my Georgia DL in 2002, at which time SSN was not required. I was given a standard five year DL although the nonimmigrant work status I had, at the time, was only good for three years. When I renewed the license after five years - by mail - they asked for SSN and I supplied it. I suspect before that time, the Georgia DL database didn't have information on my citizenship status. Whether it pulled this info from the SSN database when I gave them my SSN, I don't know. If not, then I expect there won't be any problem over my voter's registration. I sent in my registration a couple of weeks ago, so the outcome is as yet unknown.
I think this kind of evolution is the reason why people quite often report contradictory experiences here.