If a stave is totally dried with the bark and sapwood on and you know the sapwood is sound; without bugs, fungi, etc, the sapwood of osage is as strong or stronger than many whitewoods.
In the last few years, conventional wisdom regarding bow woods and construction methods has changed and in some cases dramatically. On the osage bows I have built that I used sapwood either as the entire bow or a portion of the bow I never had a problem with the sapwood. I was sure it was in good condition but I never had a problem.