As you stated, in Florida if there is a lapse in your auto insurance the FL Dept. of Highway Safety and Motor Vehicles will suspend your driver license, vehicle tag and registration. If you are caught driving without insurance these conditions will of course be in place plus likely a citation for you to appear in court or perhaps arrest you on the spot for driving with a suspended license.
Though the FL HSMV does not state for certain that a warrant will be automatically issued, different jurisdictions might apply different rules for this. For instance in some counties if you do not send back in the car's license plates, since they are suspended, a warrant can be issued for the license plates. To find out what the rules are for your area of Florida you can contact the Florida HSMV customer service center at 1-800-922-9000.
To obtain Florida automobile insurance so you can drive legally on the streets of FL get a cheap car insurance quote.