No. There would never have been a fist fight. Sinatra would never have dared. Mario didn't have the heart.
Read "The Godfather Papers and other Confessions" by Mario Puzo himself. It explains the exact details of the incident...
"It is no secret that organized crime in America takes in over forty billion dollars a year. This is quite a profitable sum, especially when one considers that the Mafia spends very little for office supplies." -Woody Allen
"I'm going to blame some of the people in this room. And that, I do not forgive."