This would delay Georgia's economic development initially. Slaves were an important part of the labor force in the period, especially in the south when heat, humidity, and disease took its tool. This is the era that slavery was legal in the northern colonies as well, so this really puts Georgia at a disadvantage initially. Eventually if the ban lasts long enough, this will come to Georgia's advantage (as many free whites will have more political voice since there is no plantation aristocracy), but there will be a long period where Georgia does not develop as fast for a lack of manpower. Oglethorpe and future governors would need to find a lot of new settlers to make up for it.
Another issue is that it provides a safe haven for runaway slaves which will irritate the other southern colonies, especially South Carolina. That will create some political problems that will need to be dealt with.
However, it is feasible for the colony to survive. Slavery was only permitted starting in 1749. If we assume the ban lasts - only thirty years later the American War for Independence begins. By the time the war was won, many believed slavery would die a natural death as it was increasingly unprofitable. By the time the cotton gin makes it massively profitable by 1800 or so, Georgia should have a large enough population of free whites to make them reluctant to establish it.
This has further impact because of potential effects on Alabama - I'm assuming here Georgians were the main colonizers of the state, and if they are "free staters" then it might bleed over as well.
Certainly even one free state in the Deep South has immense impact as to the slavery debate within the US.