You don't have to back a board bow. The grain should tell you if you back it. A selfbow will perform better than a backed bow, all else being equal. When I think of "backing" a bow, I am usually simply protecting the back from lifting a splinter. A backing like this doesn't do any, or much, tension work. Boo is not a good choice to back a bow for this purpose. It's just too much work and it is heavy. Rawhide is a better choice.
If you add a piece to the back to take over the tension work from the core, you are making a composite bow, which is different than a board bow, as it has come to be understood. Boo is a fantastic choice for a composite bow. I'd argue that red oak isn't the best core wood though since it isn't especially strong in compression. But it certainly can work.