Ask Mr. Smarty Plants

We don't know how relevant this is, but we do believe it is a matter of concern. You understand that Mr. Smarty Plants is neither a chemist nor a soils analyst. We also want to explain that the Lady Bird Johnson Wildflower Center is dedicated to the growth, protection and propagation of plants native not only to North America but also to the area in which they are being grown. Just about all vegetables qualify as non-native, either because they were introduced from another part of the world, or because they have been so hybridized or genetically altered that they no longer resemble the original plant. This means we are not experts on vegetable gardens, either, nor will those plants be in our Native Plant Database. So, we have assembled some links that look like they might be of some help to you in researching the answer to your question.

The National Society of Consulting Soil Scientists: PAH contamination of soil by asphalt.

The Journal of Environmental Cleanup Costs, Technologies and Techniques: Contribution of common sources of polycyclic aromatic hydrocarbons to soil contamination.

Concrete Paver's Guide: The Asphalt Driveway - What You Need to Know

These are all technical papers, which we don't understand, and don't mind admitting it. We would suggest you contact the  University of Arizona Cooperative Extension Office for Pima County. They are connected to a university, maybe someone there knows the answer.

Bottom line: We, personally, would not eat the vegetables. You could always have some kind of ornamental garden there; it might still be absorbing contaminants but if no one eats the plants, there would be little cause for alarm.