I also live in GA and my tenants vacated before the court date - eviction had been filed. I still went to court to complete the eviction - the tenant did not show up. My lawyer said to change locks after they left but before court date (and award of possession of my house back).
I think you are on the hairy edge of the law - but I am no lawyer. I think that you should keep their belongings for awhile.
From the GA handbook I found it says that -
"The safest course of action is for the landlord to wait until rent is past due and file a dispossessory affidavit and obtain a court order for possession of the property. This will protect the landlord from liability if the tenant claims they had not abandoned the unit and their personal items. If the landlord does remove the tenantís property without a court order, it is a good idea for the landlord to take pictures of the property disposed of in case the tenant raises a claim against the landlord."
You are right the law is not clear on what happens when they quit. I would keep their stuff, take pictures of everything, and use that if they ever decide to sue for constructive eviction. Ask a lawyer to be sure.
I still feel stuck in this situation. The house is almost ready to rent again but I feel like this situation is not completed. I plan to put an ad in the paper tomorrow and move their things to storage.