With the knowledge that they either don't have or refuse to provide GA id, I would not sell the gun unless they come up with a valid GA drivers license. I understand the pressure when you want to sell something, but guns are a little different even though they shouldn't be. Or, I would simply insist that the gun transfer be handled at the local FFL dealer with all paperwork completed.
Had the whole deal been made without the knowledge, then I would probably feel okay about the transfer/sale. However, at my age, I really prefer seeing some sort of ID with a gun transaction.
If I had to guess, they are probably GA residents or are technically a GA resident but have not gotten a drivers license, and simply don't want any record of them buying the firearm. There are many people like that and you see it on the forums all the time...... ask for ID, forget the sale..... My feeling is that I don't need the sale bad enough to take chances. I would rather landfill the gun. That of course is a bit ridiculous as you can just find another buyer but may end of selling the gun for less.
If I were selling one of my guns locally and advertising, I would simply make the ID a condition of the sale. IF people have a problem with that, then they won't contact you to purchase.