I have a court date in Florida. Could I be taken into custody during that appearance over a theft warrant in Georgia?

It's a possibility if they have a reciprical agreements which is likely as they are neighboring states. Assuming Georgia has a fugative warrant out on you. I know people that were taken into custody during a traffic stop in VA over a Warrant in MD pending extradition proceedings... and it was over a contract dispute of all things..

Yes, if Georgia is willing to pay for your transport.
Where are you living now, do you have to drive though GA to get there also.

I'm in Georgia now. Have to drive to Florida. So, they run ncic checks during court, or how does that work?