How would the story be different if the grandmother had not recognized the misfit?

I just read a summary of the story, A Good Man is Hard to Find by Flannery O'Connor and I think that the family would have been alive had the grandmother not recognized the Misfit. 

Instead of begging for their lives when confronted with the Misfit and his cohorts, grandmother recognized him and declared him to be a good man from a good family and good men don't shoot ladies. However, her plan backfired because the Misfit was an escaped convict and he is a wanted man. He did not want anyone to pinpoint his whereabouts and bring him back to jail.