Yes. The cows would never be considered organic. You can't make organic an animal that's already been treated with an antibiotic, hormone, or something just by letting it sit for three years.
Generally the cow herd would not be considered organic, unless you could prove that during its whole life it had never received any kind of a treatment, but the offspring could be. The animals born could go through that period and then be slaughtered as organic, depending, of course, on the feed and the land they're being raised on. It's quite a challenge.