I probably would avoid putting edibles in the vicinity of exhaust fumes. Even if the food were safe to eat, it might have an unpleasant taste from the fumes.

I do, however, use strawberries throughout untrafficked areas of my yard as a groundcover because it performs that function so well in addition to providing food.

You might consider using a non-edible groundcover, such as a low-growing veronica, along your driveway if veronica grows well in your area.

My grandparents have a raspberry tangle lining the driveway, it's quite common where they live (Monterey,CA) to have this as yards are quite small. The berries still taste great, and as an aside, the berries host a large preying mantis colony ! So no pesticides needed. paradise, eh? Monterey. Maybe I will move there to retire :)
PP

To keep things in perspective, as a rule with the presence of catalytic converters cars have cleaner exhaust systems compared to lawnmowers and chainsaws. Unless, your driveway has lots of traffic, I would not be too concerned about fume contamination of plants bordering the driveway.

You might try ground cherries. They are in a husk, thus somewhat protected from exhaust fumes.

Some cars are really clean now, if you have a newer model than it's putting out less crap than your lawnmower, leaf blower. Plant something to eat!