Although I had requested an extension before my visa expired I have not heard back from the government.
I need to go to Italy in August, & wish to return to NYC in September. Will I be allowed to return if my visa has not been renewed by then?
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If you want to return in M-1 status, you'll need a new M-1 visa. This is true even if your extension request is granted before you leave the US.
Normally, you can get that visa while you are in Italy, but I do not know whether restrictions related to the coronavirus will prevent or delay the process. You will also have to consider the possibility that the current travel restrictions may still be in place, in which case you'll need to find somewhere else to stay for 14 days between leaving Italy and arriving in the US.
The above takes your question at face value, but perhaps I shouldn't do that. Keep in mind that there is a distinction between visa validity and status. Your extension application was an application for extension of status. If your visa (that is, the sticker in your passport) is still valid through your anticipated return date, then you won't have any problems at all other than the coronavirus restrictions.