Is a notarized document legal if resides at is a Post Office number?

The notarization of a document is not necessarily a testament. Notarization is merely a witnessing of said document.

For example, if you found an old letter belonging to a famous film star and the content of the letter states that the film star is in love with another film star; to make a copy of the letter and pay to have your copy notarized: all this would do is make confirmation that the copy you made is a true a accurate representation of the original. (you would have to have the original to produce as evidence).

If you wrote a letter that said your address was in a cave deep inside a mountain and you chose to have your affirmation (letter) notarized, all the notarization would do is acknowledge your signing the statement in the presence of the notary is correct. In other Words, it acknowledges what you claim, but it does not make it true.

If you wrote a letter saying you reside in a tiny little box, in a massive building of tiny little boxes, in a massive town and you had your letter notarized, people might believe your statement to mean that you live in the Bronx, East London, or Los Angeles, but it's doubtful anyone would accept that you are living a life of luxury inside a letter-box somewhere.