Is Michael supposed to be Francis Ford Coppola?

Is The Godfather saga supposed to be an allegory for Francis Ford Coppola and his family with Michael standing in for Coppola himself? Talia Shire (Coppola’s sister) plays Michael’s sister. His daughter Sofia plays Michael’s daughter. Part of me wants to think that Vito represents Carmine (Coppola’s Father). Vincent who rises to power is Michael’s nephew, and Nicolas Cage was rising in stardom in Hollywood and is Coppola’s nephew. Is Jason Schwartzman going to have a character if Coppola makes a Part IV?