Any FAA Part 61 School who is not Part 141/SEVIS approved will have no clue as to the USCIS regulations on immigration requirements.
That is why they are NOT SEVIS approved to issue I0-20 paperwork for a visa.
What are your longer term intentions once you have a FAA certificate - back in Italy if and when the new EASA rules come into force - when the FAA certs may become 'worthless'?