I've read that UV is effective only against the free-floating parasites that are a part of the ich life-cycle (makes sense). In other words, the parasites not attached to fish might be affected.
There are a couple caveats, though. The parasites can lie dormant in substrates for a very long time, and there's the real possibility that parasites can spread without ever passing through the sterilizer. So while a sterilizer could be helpful, that doesn't guarantee it'll be effective, and it can be harmful as skinz78 said.