I don't think they'll send it down the pipe, or be successful if they try. The process tends to have to start at the lower courts and work their way up. In all likelihood, lower courts would simply strike it down, and the appeals court wouldn't see any reason to change that.

There are ways to skip those intermediate steps, and they could certainly try to invent a whole new process just for the case. But when one of their biggest allies on the court has a clear reason to be against it, why even try? They have a hundred other cases they'd rather do to hurt people. If you follow the domino metaphor in OP, then Loving is way towards the back.