I've read about how poorly Italian immigrants were treated in the US, but did it apply to all Italian immigrants?
Could you specify what you mean by "treated poorly"? Things weren't all roses, rainbows, and sunshine for Jewish immigrants either. Much of the same economic issues and discrimination happened to a wide range of immigrant groups, including both Italians and Jews.
Anyway, this question isn't very answerable. The overwhelming majority of Jewish immigrants during this period were from Eastern Europe. While there is a Jewish community in Italy, I don't know of any significant migration from Italy to the US. While I don't have anything that says "there were no Italian Jewish immigrants to the US", it's not a substantial community in the US.
I did some looking around, though. As I said, the number of Italian Jews in the US is relatively low, and finding lists of names like this one, the overwhelming majority moved during the WW2 era. The exception is La Guardia's mother, who was from Trieste (which is part of Italy now, but not when she lived there), and Eydie Gorme, a singer. Reading some articles on here, it seems she identified more as a Sephardic Jew than an Italian, since one parent was from Italy and the other from Turkey--her home seems to have spoken English and Ladino, not Italian. They also lived in the Bronx, which was a heavily Jewish area at the time (though there may have been Italians there too, I honestly don't know). So early on it seems that Italian Jews were Jews in the US, and less Italians. Articles seem to refer to her as the "daughter or Sephardic Jewish immigrants". But that's based on exactly one person.
So in summation, the migration of Italian Jews was quite small relative to the number of non-Italian Jews or non-Jewish Italians, making this question rather unanswerable.