I've seen a few bikes that have a screw through the tensioner bracket and chainstay tube, and it seems like it would be fine. I would jsut make sure it wasn't too big of a screw so you don't compromise the strength of the chainstay.
I don't suggest doing what I did with my bike by accident, which was tightening the bracket so much that I pinched the chainstay tube. It worked and the bike still seemed sturdy enough, but don't do it
.