No, it is not advisable to try and skirt paying the taxes due in one state on a vehicle or try to pay less in taxes by titling a car in a different state. While we are not well verse in all states' laws this would be considered fraud in most states if you purposely do so in order to avoid taxes that a state requires on a vehicle.
Many states have a hotline for people to report motorist that live in one state but have out of state plates so as not to pay in state taxes on the vehicle. This is done so that the state can catch individuals that are "cheating" the state out of their tax money.
As for the car insurance aspect, you normally need to register and insure your vehicle in the state which you live and the vehicle is garaged. If your car was titled and registered in Florida you would be required to have Florida insurance on it. Most Florida insurance companies would be curious as to why the car is garaged in Georgia but titled in Florida and may not offer coverage since car is not residing in FL.
If you need a quote for Georgia or Florida car insurance, follow this link.