YES! yes let the hydroponics take over! You can use sunlight or have the jars next to your Aerogardens for their light. I have mine in a fishtank with a cheap LED grow light b/c my cat wants to eat everything that is green. And there's no dirt. Dirt is so last century.
This explains Kratky and other methods a bit more
It's def one of those hobbies where you get a thing, like the aerogarden, and then a door to limitless opportunity opens! Except potatoes, I think root vegetables are the hydroponic limit.