I would strongly urge you to not put the sinew on too early. And by too early, I mean on the trunk of the tree while it is still standing in your neighbor's yard waiting to be cut down. I ain't joking, any idea what a pain in the keister it is to try to unwind sinew fibers from the chain of your saw???
Dang, son! On a green stave, it will work as bark or a high grade sealer to keep the back of the bow from cracking/checking. It can be done.
HOWEVER, sometimes there is wonky grain underneath and as the sinew stays slightly damp from the wet wood, your lateral stability is not excellent and you can have problems with string alignment thru the handle. I would recommend that you get it mostly dry and to floor tiller first.