Can plants be planted over a drain field?
It really depends on what you want to plant, but generally you do not want to have anything but grass or something that has shallow roots and does not block out the sun.  Your leech field works in two ways, one is the water leeches through the soil, but the other way that it works is evaporation.  Evaporation accounts from 30 to 70% of what goes in your leech field, depending on how it is designed.

So I would avoid putting to much around it or over it.  Trees will love the water, but eventually clog up your field.  The worst, ficus trees, they should be called ficus weeds.