If I have a tag and the animal is suffering I'll put an arrow where it needs to be to put the animal down. If the animal was recovering (such as the case you've mentioned) I would have to decide at that time. If he looked otherwise healthy and was recovering then I'd likely let him walk. A lot can be told by the animals body language, what it says will determine how I react.

If I don't have an open tag there is little I can or would do. The law is the law and a warden is unlikely to be sympathetic to the animal or myself if I'm in violation.