No, notarization is not a requirement in any state or territory.
Here’s the background:
In 2009, when the original UOCAVA protecting overseas voting was amended by the Military and Overseas Voter Empowerment Act (MOVE), it was mandated that overseas voters and military voters do not need to notarize their documents.
The reason for this was because the notarization process abroad is vastly more complex and expensive compared to the process in the U.S. The amendment removed a major burden that many voters faced.