I believe it does work but Ryze is better laner than he is a jungler. His clear is pretty bad pre-6 and he can't really get farmed up to get some mana etc. in the jungle.
I personally love unconventional junglers and this idea sounds awesome. Unfortunately with the op jungle creeps of this season, he might not be able to survive in the jungle. You do have some kite potential with your Rune Prison but it might not be enough. If you were to do this i would suggest getting the Rangers Trailblazer with the magus enchantment and then rush Rod of Ages to survive.
TL;DR viable but wouldn't recommend.