I have seen this done by bringing the backing to the front for binding but not the front to the back. I don't see why you couldn't do it though. There are several good tutorials on this. Google quilt self binding or binding back to front and you should get numerous links on how to do this.
As far as the raveling goes you quilting will hold the quilt in place and raveling shouldn't be a problem. The batting gives the quilt body but it is the quilting that keeps the layers from moving against each other much. If you use flannel for the batting be sure to pre-wash it because flannel has a tendency to shrink more than other fabric or batting.