Usually they live and heal over. Buddy of mine did this last season or 2 seasons ago and we found the arrow and it was covered with blood and fat. We could not find much of any blood on the ground and never found the deer. We think we found it in the spring while shed hunting but the yote had it pretty tore up and we couldn't be 100% sure it was the buck he shot in the previous fall. If it was he lived for a while and made it about 3/4 mile from where he was shot but would have looped around making it a couple miles to where we found this dead buck.
Looking at that arrow I would say it is a brisket shot deer. Buddies arrow looked identical to that arrow. Fat clogged the holes and he is either filling up inside to die slowly or he will heal and be just fine. Hard to say but with that much fat, your not going to find any blood trail.