I would suspect that pushing the animal would keep the lung from clotting and possibly healing. It has been said on here ( I have no experience of my own on this) that single lung hits can heal or that a deer can survive a single lung hit (live with one lung?) so maybe pushing and causing more bleeding and exertion would hasten and ensure death. The one thing I would worry about is how could you be sure that you only got one lung and no other organ.
I'm not too sure about that one. We trailed a doe fawn that was shot In the morning for 8 hours one day with a one lung hit chasing her around and around and finally said the heck with It and came back the following morning and she was dead. We had no Idea she was lung shot, she showed no sign of It what so ever. We figured It was a high hit above the spine.
Best thing Is to not start to early on a one lung hit. To many people do this all to often and by by deer![>:] We got lucky because we had snow otherwise we would of never got that deer.