The results are mixed.
It's well known that in general people will consider themselves above average in most areas, and driving is no exception Do expert drivers have a reduced illusion of superiority?
Expert police drivers rated themselves as superior to equally qualified drivers, to the same degree as novices, Cohen’s d = .03 ns. Despite their extensive additional training and experience, experts still appear to be as susceptible to illusions of superiority as everyone else.
Drivers' Ratings of Different Components of Their Own Driving Skill: A Greater Illusion of Superiority for Skills That Relate to Accident Involvement also suggests that good appreciation for hazard perception results in higher self-percieved safety even when skill is controlled for:
Also, ratings of hazard-perception skill related to self-perceived safety after overall skill was controlled for. We suggest that although drivers appear to appreciate the role of hazard perception in safe driving, any safety benefit to be derived from this appreciation may be undermined by drivers' inflated opinions of their own hazard-perception skill. We also tested the relationship between illusory beliefs about driving skill and risk taking and looked at ways of manipulating drivers' illusory beliefs.
Age differences in male drivers' perception of accident risk: The role of perceived driving ability suggests that younger (male) drivers consider themselves equal to older drivers, youunger drivers are involved in more accidents:
Although young drivers' estimates of accident involvement in the next year were higher than those of older drivers, young drivers gave lower ratings of accident risk for specific driving situations which demanded fast driving reflexes or substantial vehicle-handling skills. Young drivers rated their own risk of an accident and driving abilities as being the same as for older drivers. However, they saw their peers as being significantly higher at risk and having poorer abilities than themselves.
The article Confidence in, and self-rating of, driving ability among older drivers suggests there is no correlation between confidence and driving performance for older drivers. This seems to go against most results but other studies were not focused on older drivers.
No relationship was found between confidence and adverse driving events or driving performance. Understanding the relationship of confidence and self-rating of driving ability to driving patterns, adverse events and driving performance may provide additional insights into identifying older drivers at increased risk for problems and formulating intervention strategies to help lower risk.
Overall it appears that young drivers are likely to have excessively high confidence in their own ability. There isn't much evidence to suggest that higher or lower confidence actually correlates with a specific skill level. Older drivers seem to have better driving skill and less overconfidence, but I have not seen results controlling for age and correlating driving ability with confidence except the study on older drivers which showed no correlation.