A 'tender' or dinghy is not excluded from any state registration that I am aware of. Most states require any vessel with a motor to be numbered, and some states even require registration on non-self-propelled boats if they are a certain length. Documented vessels are excluded from state motorboat numbering requirements - but the state may require that they be registered, and many do. A documented vessel's dinghy is not covered by the Certificate of Documentation, so a state's regulations would apply.
More info about Florida registration can be found here
Hope that helps.