I searched through the New York Public Notary Law www.dos.ny.gov; then I went through the Dept. of Licensing and just called them.
I found the 21 page law and it seems it is a violation if a notary signs papers outside his jurisdiction, namely a county in NY. Violation is 142-a, Sec. 2 f I think. It is also fraudulent and forgery knowing that the parties to sign were physically not in the state of licensure.
The document can be nullified in a court of law.
Please advise if this is true in another states as well.