Very few of those who would be carrying everywhere would have the kind of training needed to be effective at stopping crime, even if they were to be around it.
It would be hard to come up with numbers to back or disprove your statement.
Read “The Armed Citizen” columns. Lots of evidence.
There is some research showing self-defensive gun use is not associated with a lower risk of victim injury during a crime [0]. If training levels were generally high, I'd expect people who use guns in self-defense to be more successful in preventing injury.