I'm a diamond Katarina (mid) one trick pony who climbed from silver to diamond in season 7. I have a lot of experience with reworked Katarina and know what it takes to win games with her. Overall my accounts I have around 800K mastery points with her. If you'd like a sample of my experience with kat, check out my Youtube Katarina highlights at: https://www.youtube.com/channel/UCljwcdKelh2qXo78mXGVaDg
I also stream from time to time at www.twitch.tv/hockeygnome , feel free to stop by :)
My accounts (NA): MasterTheDagger , ChumUrMum , Katarìña

In short, no. Katarina is not a jungle champion and is outclassed by most other junglers in the game. Katarina provides nothing else for the team except for damage, which is why her best role is mid lane. I recommend only playing Kat Jungle for fun in a normal game unless you are a Kat main. Kat's second best role is top lane, not jungle.

I carry the same runes as I do when I play Katarina mid. Electrocute is arguably the best keystone to take on Kat, as it offers high burst potential which Katarina uses all the time. Another option is Dark Harvest which is easier to stack than mid lane kat, as you'll be clearing large jungle camps all the time. However, I feel like Kat jungle relies heavily on her early game threat, which Dark Harvest doesn't give as much of. Eyeball Collection lets you snowball harder than zombie ward, but take it if you want it. Ravenous Hunter is my favorite out of the Hunter masteries, it gives you a lot more to work with when fighting, as Kat is very squishy. But the option is still open to go Ingenious Hunter for more damage in mid game fights, or Relentless Hunter for faster rotations.

For the secondary tree you can either go Sorcery or Precision. Sorcery will help with early game cheesing, but precision is much better for mid game fights, which is Kat's strongest point of the game. Triumph allows you to heal for a large amount of HP after every kill or assist, which goes perfectly with how Kat can melt people in fights. Coup de Grace is non-negotiable with precision, it helps you kill people faster than the other runes. If you do decide to go Sorcery, you will want Absolute Focus and Scorch.