Well, it is possible to not naturalize but still have a Declaration of Intent somewhere. I have seen that before. But assuming they never even began the process, you are going about it the correct way by collecting all the other relevant information. You can also have New York state issue you ...

Have you looked in the localities where he lived to see if he perhaps filed any Declarations of Intent(ion)? If you can find one of these and they are after your GGF was born, then you know for certain he was not naturalized until after the fact.

I know that I can request the extract of a marriage/death/birth record from the comune of Napoli. I have read on their website that I must write them a letter to here:

Comune di Napoli
Servizio Stato Civile
Ufficio Corrispondenza valori
II traversa privata via dell'Epomeo 80126 Napoli

But I am ...