No, the seeds if they are not washed away will rot.
You do need to start them in trays first. You can use oasis blocks for hydo. The blocks will not come apart with the stream of water in a rail or net basket system.
Peat lite media can be used to start plugs in a tray and transplanted to a media bed (like hydroton or cinder) or you can still use the oasis plugs. Fine particles like peat moss and dirt, you want to avoid because it will eventually plug up your filters and your system. Even media beds eventually get plugged up with accumulated roots, media and dirt and have to be flushed.
Whether you use a controller or manually test the nutrient solution daily, plants still need the same things. Seeds do not need nutrients, they have all they need to start within the seed. What seeds need are air, light, and water. If the seeds are under water too long, there is no air and they will rot. You could start the plants in media and clean off the soil and then put the plant in the system, however it will be hard to wash off every bit of soil, any particles that remain will get into the system. If enough get stuck, it will clog the system. Plants in hydro, aero, or aquaponics have two kinds of roots, water roots that are in contact with the water and air roots. Water roots cannot dry out or they die, for water roots to stay alive the water must be well aerated or streamed so that some of the roots are able to still be outside to take in oxygen, air roots don't like to be in water all of the time or they will rot and die.
Usually the plugs are planted with one seed in each plug. The plug is put inside of a tray that is bathed by the nutrient solution and the solution is not allowed to sit. It enters from one end and drains out the other. The tray is slightly tilted to encourage drainage. The plugs stay wet all of the time and keep moisture around the growing plant. The roots at the bottom of the seedling will be more accustomed to being wet so they will be the water roots. The roots at the top of the plug will be moist but not directly submerged in water all of the time so they will be the air roots.
The plugs get put into a small net basket and inserted into the system. The place I work uses rail and aeroponic towers for hydro and cinder biofilters for aquaponics. All of the systems eventually have to be cleaned. The roots from the plants get very long and the rails need to be cleaned of the accumulated roots. The nutrient system encourages algae to grow. The hydo are all in enclosed houses because some of the cultivars were developed specifically for hydro or greenhouse and do not stand up to pests well, so they need to be protected. It is very difficult to control bugs or disease in these systems. You will be limited by what you will be able to use and the close proximity of the plants will mean that problems will multiply quickly. When it gets really bad, your only recourse would be to destroy the crop and sanitize the system.
Happy gardening in Hawaii. Gardens are where people grow.