If you’re interested in shipping seeds or herbs through the mail, it certainly is possible. With the number of nurseries and greenhouses around, I’m sure it’s done every day.
The best method for packing green plants for mailing is to use damp newspaper to cover the roots and plastic bags to retain humidity around the foliage. Check these links for great explanations:
The best tip is to make sure not to get the foliage wet. If the greenery does get wet, tamp it with paper towels and let dry before packing in plastic bags. Any herb leaves that are wet during transport will rot.