If it does you won't notice it. But be sure to give the rawhide and wood time to dry afterwards. I would let it rest 3 or 4 days after adding the rawhide just to be sure.
What glue are you planning to use? If you use TBIII put a thin coat on the back of the bow and let it dry completely. When you add the rawhide the first thin layer of glue will act as a moisture barrier to prevent most of the moisture from getting into the wood.