Does anybody know for certain if in the State of Georgia, an HVAC ("conditioned air") license is required in order for a homeowner to install their own HVAC system?
The type of unit called a "package unit", where the condenser and air-handler are combined into a single outdoor unit comes from the factory already charged.
That solves the refrigerant side of the equation. Don't actually know if that is sufficient in Georgia or not.
Some un-named individual who lives in my house in NC installed one of these and, so far at least, has gotten away with it.
Refrigerants are controlled by the EPA, so a license is required for charging the system in any state. However, the installation is not regulated.
You should contact your local building department. They'll be able to definitively answer your question.
Though I'd be surprised if a homeowner had all the tools and knowledge, required to install an air conditioning system themselves.