That would not be a great idea, and would be much easier to mess up. You have to push the nail gun into the animal to release the safety. Rabbits are pretty skittish already, and have a small brain and a small spinal cord. I prefer to put a piece of rebar over there neck standing on the rebar on either side. I then put the front feet of the rabbit on the rebar grab the back legs and pull hard. Its quick and easy. I have found that if I don't set it down right away it doesn't do death throws either. I want to make a rabbit ringer type device because I feel that it would be a better choice.
On using a .22 to dispatch bigger animals. I aim for where the spinal column and base of the skull meet. Its an easy place to see and aim for. I have only had one animal that didn't die instantly doing that. It was a very fluffy and skittish sheep. But the .22 at that close still knocked it out. This allowed for me to cut its throat. So it was still a quick humane kill. I don't think a nail gun would have that same effect if you didn't hit it dead on. I find that killing isn't always the easiest thing for people, and the cleaner the kill the less emotional trauma there is.
On another side note my wife just wrote a really good article discussing some of the emotions and difficulties that come along with raising and butchering your own meat. On Loving Your Food: A Pig in Review