Yes, it does work in FL, and yes, if you close the box with the Avis transponder and use your I-PASS, that's what's going to be charged.
You will need to add the license plate, though. Right when you get to your rental, sign in to your I-PASS account and add the vehicle. If you do this right away it'll be in the system when you're heading out. Don't forget to remove it again upon returning it....