Yep the whole plant is safe to feed, but as Mudgy says could cause a bit of windypops! :lol:
The leaves are a FABULOUS astringent feed for bunnies. Mine love the leaves and you can feed them fresh or dried - they dry very well. If you've got a friend with a whole load then ask them to cut the stems down (they will die back over winter anyway) and dry all the leaves - you lucky thing! Mine didn't do so well in our poor soil but in good soil the plants can grow up to 8-10ft!
A couple of years ago when Poppy had an impaction jerusalem artichoke leaves were the ONLY thing she would eat for about 2 days!