Yes, the novel and the film portray Vito as having stumbled into the life of organized crime. This was a very effective device to give us a good feeling for the downtrodden life of Italian immigrants (as DC said) and Vito's determination to rise above it.
In real life, it would have been inconceivable that, in 1919 (when Vito kills Fanucci), New York's Little Italy would be such easy prey for a young upstart like Vito. GF shows Fanucci "running" the neighborhood essentially on his own, with just a "license" from a bigger Mafia boss. The novel has a scene in which, after the Fanucci killing, Clemenza calls on Vito and says, "Nobody is collecting" from the gambling, etc., that Fanucci shook down. So Vito steps into a vacuum. In real life, there would have been no vacuum--and no upstart like Vito.