It looks like tenders must be registered if used for other than emergency purposes (at least in North Carolina, I imagine it is similar in all states). Just goes to show you that if you act confident, the laws are so complex that the people enforcing aren't even sure of all the requirements and exemptions.
"IS THE VESSEL TENDER DOCUMENTED?
Documentation of your vessel does not cover the vessel's tender or dinghy. These craft fall within the jurisdiction of the motorboat numbering laws of the state of principal use. Please contact your state agency that handles the registration or numbering of motorboats for further information"
"Ship's lifeboats or dinghies do not need to be registered if they are used only for emergency lifeboat purposes. However, if they are motorized and used for non-emergency purposes, they do require registration."