There are lots of artifacts in the national museums where the NA's did exactly that, even including arrows (especially the fore-shafted types) and utilizing the stone heads. I have seen a lot of artifact photos of various tools such as axes, knives, hoe's, adz's etc where the raw-hide was the only haftment. Also have seen them (artifacts) where it was all pitch, raw-hide and pitch, and just plain raw-hide.
Hope that helps ya some.
rich