Can you wash your hair everyday if you only use conditioner?

I work out every day (trying to get back in shape), which means I have to shower everyday and wash my hair everyday. I know it's bad to wash your hair everyday because it can strip your hair of its natural oils, but that's really only the sulfate-filled shampoo right? So if I follow this new "no shampoo" regimen I've heard about, where you only condition your hair b/c it doesn't strip your hair of its natural oils, will washing my hair everyday with just conditioner be alright? Will it still strip my hair of its oils and leave me with greasy hair if I skip a day?