No, not really.
Are there elements of the Jewish stereotype in it? Sure. I think this is more representative for old world Russian Jews. It certainly has nothing to do with modern Jewish people.
I will say this, though.
At almost every Bar mitzvah, you will hear "Mazel tov", someone sing "Sunrise, Sunset". You will see the elements of a Jewish wedding as portrayed in the musical. You will also see the same type of patriarchal family structure in most Jewish families today.
Only in the most orthodox homes will you hear of match making or some of the hard pressed traditions stressed in the show.