Is she even viable in the jungle? I really don't think so but i want to hear some opinions.

No CC, no sustain. Why... why would you WANT to?

I doubt you could do it. Unless you had a full rune page of armor and started cloth armor + 5 hp pots. Even then it would be INCREDIBLY slow and would guarantee a loss for your team.

Might be possible with Spell Vamp. or Hp/5 Quints. The ganks would be amazing, particularly bot lane, or counter ganking. On Stonewall008's channel, he has a clear time of 3:45 which is pretty bad on average. It might be possible with HP/5 or Spell Vamp. Quints.

Mainly I see it being a really good combination with certain other teams. Say you had Taric, Ezreal bottom. Through Katarina into the mix, quite literally any time everyone's ult is ready, pick up a free kill. Or if you had Annie mid, and could stun for 1.75 seconds pretty much any time. That could get stupid real fast with Katarina's Death Lotus. I hope someone looks into this.

if you could solo minion camps, you could pub stomp

Possible, but not viable. From a friend who has tried, she suffers from slow clear time and vulnerability. On top of this, you'd likely have to gimp her runes/masteries to pull it off. Leave her in a solo lane.

I did it randomly in a solo-q normal blind pick game the other day with normal Kat runes and 9/21/0 masteries (but not set up for jungling, I had to pick a suitable page at the last second because my team was a bit silly). They stole my red and wraiths instantly and I was really far behind on everything. I was able to solo camps even starting boots3, although I did have to buy an early cloth armor anyway. We won. But not exactly because of my presence (I went 4-4-12 eventually but the power of her ult even without too many items did let me set up a lot of kills on ganks). ;p

Diana does the same thing (ap-based assassin who can clear the jungle) only better.

I do it all the time. She is very weak until level 4 though. You'll want your team to help you damage the first buff, and then take the second buff for yourself. Be extremely cautious of invades as you take your second buff, since you'll be extremely low on HP afterwards.

Besides that, she actually has one of the fastest clear times in the game (focus W). Her ganks are very powerful and she can snowball really hard. I prefer to build her as a hybrid when jungling, but you can still use the traditional AP build if you want.

personally I think you'd be better off staying mid, pushing the lane a lot and then going roaming, either to counter jungle or gank top/bot. I can see the desire to jungle with katarina.. she's one of my most played champs so I know just how good she is at clearing camps from level 4+ and generally roaming (high base movement speed for example).

If I were to try to jungle with her, I'd go phsyical damage reds (and maybe quints.. though I do love mov speed quints on her), yellow armour and MAYBE blue armour (though more likely MR/lvl instead (or ap / cdr.. would need to experiment), start wraiths, then red with a hard leash + help with damage on it where possible.

I presume you'd go Q > W > Q > E spell route, and probably play a 9/21/0 type masteries.

anywhoo overall, I'd say stick to mid and then roam once you hit 6 or so.