Instead of using the usual hickory or boo for backing an osage board would rawhide be acceptable.
For protecting the back it will work fine, in fact you can cover the rawhide with plastic wrap and use another board on top with clamps or even stacking bricks on top for a press
Yes it should work, I've backed both hickory and ash with it and have read about others backing less than perfect osage boards with it
Craig, I built a couple of wood bows back in 1994 one was mulberry the other Redoak(board). I used deer rawhide it's thin, strong and worked well.
You will not get the same effect using rawhide as you will using hickory or other wood backings.
You could but burlap, silk or linen would be easier to install. Ot's a board and boards are inexpensive. More on my site. Jawge
http://georgeandjoni.home.comcast.net/~georgeandjoni/