Unless you have a violated back ring, a swirling grain or you just want a rawhide backing it probably isn't necessary. Mulberry is an excellent self bow wood and usually with thick rings. I normally would add a rawhide backing after tillering or about half way through it. You want to be sure no corrections with heat will have to be done before you add the rawhide.
On an osage bow I am working on now I added the rawhide backing early, before I stressed the bow because this stave has very thin rings and I couldn't get an un-violated back ring. In many cases, rawhide will not add any additional draw weight. I guess if it is thick enough it might but it's physical weight would eliminate any advantage from the rawhide. Pat