I think that would work well if you covered the outside to keep it quiet and probably inside as well.If you pack up your bow,you will have to do something with your arrows as well.
It is always nice to be hands free,especially in steep country but you also have to ask yourself if you may need the bow while carrying your pack.
I bought my first takedown recurve in 1972 when I was an avid backpacker.I soon found that it was just as easy to carry the bow,strung,and there was always the potential of running into game on the trail.
I have been working on a setup to carry that same bow in my cat quiver pack for lion hunting.
I found a large,padded,zippered knife case(19")that my riser fits in.I got a fleece long bow sock for the limbs.I cut the bottom out of the sock and tied a knot in the center of it.One limb goes in each half of the sock and I can shove them all down in the pack.The curves of the limbs have to stick out of the top of the pack zipper but they lay across the top of the pack nicely.
I do like the idea of having my hands free in the steep country where we have been lion hunting and the bow won't be needed till a lion is treed and many days it won't be needed at all.