Another extremely common question when it comes to small in-home hydroponic gardening, is "Can I use organic fertilizers?"
Unfortunately, the answer, while not an outright no, is a very stringent 'it's not a good idea'. This tends to upset people if you leave it at that. But just because organic fertilizers aren't a good idea, doesn't mean your plants will be any less nutritious and healthy for you!
The problem here, and the apparent contradiction, is that "organic" has specific meanings in specific applications. It has unfortunately, however, become a 'buzz word' used by people to just generally mean 'natural' as opposed to covered in synthetic chemicals, like pesticides. In this situation, though, "organic" is really no more nutritious, and is not a particularly safer, better, or more sustainable system.