I know a few kids who went to those types of schools. None of them had miraculous changes in character, although the experience wasn't entirely detrimental.
Most of those places are extremely expensive. Tens of thousands. But it gets the teenager out of your hair for a while, at least, and gives you all a break from each other.
I don't know of that particular school. If you can get positive recommendations for that school or another, and you can afford it, then I think a place that offers positive, strict male mentoring for a teen boy will be definitely worth a try. Most teen boys need a strong male mentor. Their spirits cry out for it. If dad can't do it, then someone else is worth a try.
Good luck, the teen years can definitely suck. But there's usually light at the end of the tunnel.
And I don't think that sending your teen away for a while is the end of the world or is "giving up" on him, as some below suggest. Why does a teen need to live with mom all the time? Sometimes moms can only do so much, and their teens are happy to be away from them.
BTW -- This does not need to be presented as something punitive. Why is going to school in another state for a while a bad thing? It can be an adventure. Rich people send their kids to boarding schools all the time. I don't think you present this as a punishment. He's obviously not interested in what he's currently doing, so there's no reason for him not to try this. He's 15, not 5. Anyone who doesn't understand feeling "done" hasn't parented long enough, or parented challenging children.