With edibles, there is a risk of pathogenic contamination, so I wouldn't recommend it. It does pose a health issue, and although people do/have done it it is not a good idea. You can plant other things, like herbaceous perennials, if you want to fill in the area, but don't plant trees in the area, or most woody shrubs within ten feet, to keep the roots from damaging/clogging the system.
Here is a detailed article on the subject. Here is an paragraph from that article, concerning edibles:
Although the drain field may seem to be the ideal place to have a vegetable garden, it is not recommended. Even though different soil types differ in their ability to filter contaminants out of the effluent, there is no way to be absolutely sure that everything is being filtered out. Therefore it is not recommended to plant vegetables in a septic drain field because of the health risks associated with bacterial contamination. Also, vegetable gardening requires frequent cultivation of the soil, supplemental watering and fertilization. None of these practices are recommended for a drain field. Using a raised bed is also not recommended. The additional soil over the drain field reduces the effectiveness of the system to filter the effluent because it interferes with evaporation of soil moisture.