My boyfriend had joked about a similar cache, in putting a logbook attached to our dog's collar, and then whenever someone saw her, they could log her. Seriously though, I think a cache can be moving in order to be approved. We had a cacher in NC who would do full moon caches and each full moon he'd put the container somewhere else and it had to be found that night. He couldn't get it approved due to the movement and not being available always, so he just maintained it via a listserv for people that wanted to participate.
Edit: Adding on to that, I've seen some neat travelbugs that people had made into teeshirts so they could wear them around and get logged. For example: Shirt 1 or Shirt 2