No, you don’t. If you have a USCG documented vessel, a vessel that is documented with the Coast Guard, then you do not have to register it in the state of Alaska.
According to the Alaska Department of Administration Division of Motor Vehicles, “All boats longer than 24 feet are required to be titled unless documented by the USCG.”
That said, while “a documented boat is also exempt from state numbering… the State of Alaska registration decal must be displayed.”
To learn more about boat registration rules in Alaska, you can find the Alaska Department of Administration Division of Motor Vehicles site here.