Cool thumbring there Rob. I bet that material works pretty well too. I have a few that I made out of pieces of white tail antler. They work great but I had a few failed attempts. I learned that you need to find the right areas of horn to use otherwise you may end up sanding them into a soft spot that has give to it. Or worse yet, breaks. After all that work too :(
I'm hoping to give "thumbring" style bows a try again when I am able to afford another.
To stay on topic, as far as hunting with them ? Absolutely, go for it. As long as you are shooting well with the thumbring and consistently getting the same accuracy you feel is appropriate just as any other style hunting device you may use. They certainly worked well on the battlefield in years past so I can't see any reason they wouldn't work in the woods.