Technically if you're not using soil, it is hydroponics. Not all hydroponics systems use pumps. Passive hydroponics, like what you're describing, doesn't require any of that.

In a word, yes, you can grow exactly as you describe. Just make sure you're using proper hydroponic nutrients even though it doesn't seem like a hydroponic system. Hydroponics is simply soil-less growing, so you'll need exceptional solubility in your nutrients just like you would in a more stereotypical hydroponic system.

I recommend Advanced Nutrients. There just isn't anything better.