At minimum, you need to close off the area from the grille opening to the lower core support tie bar. Best is like the stocker that goes back to the crossmember and around the oil pan slightly.
This keeps air from dumping down under the car, especially at speed. In traffic, it also keeps your fan from pushing too much air back through the radiator/condensor and other coolers. Stand infront of your car on a hot day with the AC on, and all the fans running. If you have this cover off, there is quite a bit of air being blown forward. This is not a good idea, as those fans are supposed to pull or push air towards the rear of the car. Any air you feel being blown forward is lost energy and cooling that might cause a problem.
Last but not least, is the downforce effect you lose without the cover on there.
Air reacts much like any other fluid/gas. It takes the path of least resistance. If you place a cooler into the air flow, the path of least resistance is not to go through the cooler, but around it.
On this same note, the air that does make it through the grille opening, now has the opportunity to either go through your FMIC/oil cooler/Condensor/radiator, or just dump down under the car... Which way do you think it's going to go?
That same air is now adding lift to the nose of the car. It can build up pressure there, and since the air going smoothly over the curved hood (like the curve of an airplane wing...) creates a low pressure area, your car's front end starts to lift a high speeds.
The stock undertray smooths out the air that does get under the car, and limits the air that dumps down from the grille inlet, and forces more of it to go through the coolers where it's usefull.
This also creates a low pressure area at the rear of the oil pan, and that helps to draw the hot air out of the engine bay, and away from the car. This is a good detail too for downforce.
Low pressure always wants to be filled by higher pressure air. Always.
This is why simple vents in the front of the hood will draw air out of the engine bay. And why your car has airflow from the HVAC vents at highway speeds even when your fan is off. (The screen vents at the base of the windshield is a high pressure area, and that forces air into the car via the HVAC system since the car also has vents to pull air out of the car at the C posts. (Just behind your glass in that low pressure area.)
Many cars with frameless glass will suck the windows out at high speeds due to this low pressure area over the side glass. Our cars generally control this very well, but the low pressure area still exists.
Best option would be a undertray/splitter design. It would enhance the downforce, and keep more air going into the grille, and less under the car. Best option is to make the splitter at minimum the distance of the front bumper, and even sticking out further is better, but becomes non-streetable at the extreme.
Good thing is the MK3 is a nice areodynamic design from the start, so you really have to screw with it to make it perform poorly. (I've owned older muscle cars that at 115mph were taking off on the front end. The Supra with or without the tray is still rock solid at that speed. It is better with the tray on there however. Experiment with it if you don't belive me.) Also, due to the downforce created by the tray, you need to make sure it's attached well, or it will rip off at speed.
Good luck.