When we lived in Roswell (red clay heaven just north of Atlanta) we had a cherry tomato plant that grew 12 ft up the side of a raised patio then 20 feet along the railing on one side and was starting on the adjacent railing when frost killed it.
Our method was to plant and forget. So experience of one, I'd say that you can grow tomatoes in Ga's red clay. They were delicious. I'm not certain of date to plant seedlings, but I imagine about the end of March.
I tried growing tomatoes in GA red clay, they didn't do well. Now I raise tomatoes on top of the clay in raised beds with lots of mulch. They do great and taste is good IMHO. I raise mostly heirloom varieties. I am in the Atlanta area and I start mine in early to mid-March for transplant outside around April 15. You may want to post your question in the Georgia Gardening Forum for more opinions/answers. http://davesgarden.com/community/forums/f/region_ga/all/
Cherry tomatoes will re-seed into the clay and won't much care. However good big size tomatoes need good soil as beclu727 says. I grow mine the same way as she does. Copious amounts of organic materials, and I use only organic fertilizers too like bone meal, soft rock phosphate and fish emulsion.
Although I am having problems with some cherokee purple this year, the green zebras and Matt's wild cherry are once again going INSANE and flower right through heat for me. I have about 40 good size green zebra ripening all on one plant.
My raised beds grow more than tomatoes too - lettuce are still going in them, as are other leaf veg, we've been eating eggplant, some nice little hot peppers, .. winter squash is prolific and I probably now have 10 good size squash growing on one plant. Beans are all coming up (I was late on beans).
Georgia clay probably has good nutrients, but the drainage is very poor. And the soil may be alkaline rather than neutral to slightly acidic which is what tomatoes prefer.
I would do raised beds with open bottoms, so eventually all the goodies you are adding to the "box" such as horse, cow, sheep, or rabbit manure, alfalfa meal, cotton burr compost, shredded leaves, etc. work their way down into the soil and improve it.
Tomatoes will use all the space below the soil line if it's good soil.
Our SC clay is pretty acid, even for azaleas and rhodies to do fine. I planted some in the ground in late May (I think) and they're doing quite well. There are two plants each of Rutgers and Mr/ Stripey, and so far, so good. Two ripe Rutgers, and they were good! The Mr. Stripey has fewer tomatoes, but they're larger, and one is getting close.