Yeah, it could go either way. My buddy shot a nice buck during bow season - similar situation- hit the buck in the front shoulder with not much penetration. Another guy that hunts with us ended up shooting that buck during gun season 1 month later. We found the arrowhead still imbedded in the buck's shoulder. He looked like he had lost a little weight, but otherwise was healthy and probably would have survived if he wasn't taken in gun season.
Another time a friend's son shoulder shot a doe, and we were able to find her after a fairly long search. In that case, the arrow had penetrated 1 lung.