I don't think Leona is a viable jungler personally, and even if you could show she is capable of it-- which is more than possible given the relatively recent jungle changes which made jungling easier; there are still far better junglers than she.

Also any of those other junglers are going to easily counter jungle her, because as you point out she has no damage by herself (for the most part); so she'll either die, or have to retreat, or have to ask for help from a lane to get them out of her jungle because she won't be able to do it herself. This is nothing but a hindrance to her team, when junglers in general are the driving force that is supposed to tilt the different lanes in your favor, or at the very least out of the enemy's.

Leona isn't anywhere near a viable jungler due to these points, in my opinion.

Happy to see somebody else thinking like me here. I know I just started mine, but I decided to get Mobafire specifically to share my Jungle Leona Build. Good to know that I wasn't the first to think it.
Look at mine and let me know what you think!