Frankly there are too much variables to look at.

You could argue that cycling improves the health, which may keep people more alert as they age; while the extreme version of car culture causes drivers to become unhealthy, which their own health issues may contribute to accidents on the road.

It's not really feasible to isolate these variables, e.g. you shift x% of drivers into commuter cyclists, their health improves, less pollution, but then more cyclists mixes with drivers on the roads, etc etc...

To quote Dirty Jobs, Safety Third. We get in a car or on a bike commute to go somewhere. Just don't do stupid s*** and stay alert, whichever mode of transport you use.