No, though there is no requirement that Documented vessels be registered, although owners may register them if desired.
If Documented with the U.S. Coast Guard (USCG) and being changed to state registration – the Certificate of Documentation, a copy of the signed CG-1340 Bill of Sale, and either a Letter of Deletion from the USCG or the Abstract of Title (with proof of lien release in the documented owner’s name).
Note: Watercraft cannot be documented by the USCG and titled at the same time. The owner must choose between documentation or titling. While a documented vessel may not be titled, it may be registered at the owner’s discretion should a registration decal be desired to show proof that sales tax was paid. The registration decals may be useful if the watercraft is operated in other states that require a registration decal or other proof that sales tax was paid.
https://dwr.virginia.gov/boating/wog/registration-and-titling/