RE: Is this possible? Or am I mistaken?
Deer are amazingly tough animals. I've seen myself, and heard plenty of stories to this effect. You did the right thing, going all out to try and find the deer, but sometimes a deer will survive a hit that seems to be fatal.
I think you do all you can to recover the deer (which you did) and if you can't find it after a long, thorough and smart search, chances are, it is going to live to see another day.