You don't need plastic. Be cautious about the type of wood you are using. If it is pressure treated lumber you don't want veggies growing near it. If anything you would want to cover the pressure treated lumber with plastic. As far as the ground over the leach field you need it to breath. The plant roots will not effect the leach field and may in fact help it breath. Here is a great book to get. I learned a lot about septics this way.
http://www.shelterpub.com/_shelter/ssom_book.html
