I don't think your drain field would contain any human diseases that your family members don't already have. Think about it - where does the contents of your drain field come from? Your house, right? Maybe I'm missing something, but I don't see a disease problem. On the other hand, one of the things that helps a drain field release/remove the extra water is the grass and plants over it. If you turn it into a garden it might be less efficient.
Others might have a different point of view.

Septic systems always have the possibility of contributing to disease. The septic tank is full of rotting waste that trickles out into the septic field. The field is to let water sink into the ground and dilute any pathogens. That's why wells and septic fields must be seperated. I think putting vegetables on a septic field is dangerous. Another point is ruining your septic field. If you cut into the field, you may end up having wet spots or an overflowing septic tank.