When you add media to your grow beds they will require less water to fill. Also the three beds will get out of sync so they will be in different states of fill/drain. So the tank level will be more constant in operation than you are seeing now without media. Having said that I am a firm believer in a sump tank. I have had a leak and the sump pumped it self dry, but the fish were still swimming in plenty of water. Plus I think it is less stressful on the fish if the water level stays constant.
If you put the 4th bed in and use the 15 gal sump you should be ok. Looking at your picture I would test it by putting media in what you have now and running it without the bells in place. Measure the water drop in the fish tank to calculate how much water it took to fill the beds.