In a perfect world you'd have an airstone in the res if the roots will be resting in it, as roots need oxygen and will theoretically "drown" under water.

That being said, it won't kill your plants and I've "seen" plants that had massive root masses under water at all times in a res without an airstone and the plants were fine.

If price isn't an issue put an airstone in each bucket if you want optimized results.

With regard to your question about the Hydroton going through the holes, most planter tops I've come across have small enough holes that the corn won't fall through; if the holes in your tops are too large, somebody sold you the wrong product. It's no big deal if a few corns fall through here and there, though.