I reside in Florida and was arrested in Georgia for DUI. I am applying for a FL. Real Estate Lic. but have to provide FBI Fingerprints. Currently on probation in GA with a warrant for my arrest.

Will the FBI fingerprints show this? Will FL reject my application?

The FBI will easily show this and your application will be rejected. Would highly suggest that you clear up the warrant in Georgia as warrants don't expire for probation violations and you will be detained if you are in any kind of traffic stop.

Yes it will show up, and to be honest if you have an arrest warrant for you, and you do your prints at a police station that uses the newer electronic fingerprinting, the warrant will pop up when you are getting printed and you will be detained.

You will not be allowed a license with the warrant outstanding

You could get a license with a DUI normally they willl have to review your case, but with a warrant no you may as well spend your time getting this cleared up