Yes, Georgia can suspend your driving privileges in their state if you fail to pay a traffic citation you received in GA. Georgia cannot suspend your FL driver's license nationwide but they can suspend it in their own state for your failure to comply with a ticket by either paying it or fighting it in court.
The Georgia Department of Driver Services (DDS) says that if you fail to appear in court or respond to a citation, your license may be suspended indefinitely. This is for in state or out of state drivers cited in GA.
Once municipal court in Georgia notes that if your citation does not require that you appear in court and you fail to have it paid by the court date, your driver's license will be suspended by the state and a $75.00 late fee will be added to the cost of your citation.
This court also notes if you fail to appear in court on the court date (on the front of your citation) a bench warrant will be issued if your case requires a court appearance. You will be entered on the State of Georgia's computer system as wanted by the town's Police Department and your driver's license will be subject to suspension by the GA Department of Public Safety. A failure to appear warrant incurs an additional $150.00 fee to the cost of the citations. If an officer stops you again, and you are on the computer, they will arrest you and take you to jail.
A different Georgia town's traffic court states that if you fail to pay your fine or appear in court, a warrant for your arrest will be issued, an additional contempt of court fine will be accessed and your driver's license will be suspended. In Georgia when you do not pay your citation on time court costs plus surcharges can be applied as well as an indefinite suspension of your license so to keep from getting your license suspended and additional fees it is better to pay the ticket on time.
Also keep in mind that Georgia and Florida are part of a multi-state reciprocal agreement regarding penalties to apply if a motorist fails to comply with a traffic citation. Georgia is not part of the Drivers License Compact (DLC) which requires member states to report the conviction of a moving violation back to a driver's home state; however they still do exchange this information with other states. Georgia is however a member of the Non-Resident Violator Compact (NRVC).
The NRVC requires member states to suspend the driver's license of those who get traffic tickets for moving violations in other states and fail to pay them. So if you have unpaid traffic citations in Georgia they will be reported to your licensing state of Florida which is also a member of the NRVC. Florida will then take action against you by suspending your license. Unlike when Georgia suspends your license and it is only suspended in that state when your home state of Florida suspends your license it will be suspended in all states.
The FL Department of Highway Safety and Motor Vehicles (HSMV) states that failure to comply with traffic summons (including an out-of-state traffic summons), to appear on a traffic summons or to pay fine results in your driver's license being suspended indefinitely. To reinstate your FL after such a suspension the FL HSMV says you must satisfy the traffic summons and present proof of the satisfaction plus a D6 suspension reinstatement fee in any Florida driver license office.
So unpaid traffic tickets in Georgia can affect your ability to legally drive in Georgia because they do have the right to suspend your license there. Also your home state of Florida should be informed of the failure to comply with the GA citations and also suspend your license until the tickets are taken care of.