Thats what everyone tends to think, and I guess, yeah, its a possibility. Often times what will happen though is the rabbit will run into the snare and its neck will break when the snare tightens as the rabbit is running away from the tree. If the neck doesnt break right away, the rabbit struggling will generally keep the wire tight around its neck, suffocating it.

If anyone out there has any way of making a sort of "Stop" for the snare, so it tightens and doesnt open back up I'd love to try it out. (as long as its a simple thing to do)