I am not giving you legal advice, but a lot depends on the warrant and its conditions. In my area, I have seen FTA warrants tossed after five years due to not being served upon the person. Are you sure the OUI FTA is still valid? Secondly and to confirm, is it a warrant issued in the State of Florida? If not, they may decide it is not worth the cost of extradition and just cut you loose. I see it all the time when somebody is run and found to have a warrant from another state, yet the warrant will specify they can only be picked up in surrounding states or counties.

Lots of places do it differently, so like others have said, your attorney should be able to guide you through the process. Above is just my two cents.