Nearly every if not every champion has the capability to jungle.
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Katarina would be a lower tier jungler because her jungle clear is sub-par, has no hard CC, and somewhat squishy so sustain is not high.
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I have gotten fed as Katarina and tried jungle, and even with all the AP I had accumulated, neutral creatures still die at a relatively slow pace, but it's not TOO terrible. She isn't all that when it comes so soloing dragon as well.
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She is has no crowd control whatsoever, so when it comes to ganking, all she can bring is damage. Since she brings no CC and is squishy herself, CC can and will shut her and her ganks down easily.
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The thing is, since she is commonly picked mid-lane, and when mid-laners have the opportunity to roam, it can cause havoc if they manage to get a few kills up, and if she does, you will pretty much be deleting someones health all together early game and possibly mid game all if the enemy champions don't itemize or are not too tanky.
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A well fed roaming Katarina, jungle or not will not be pretty for the opposing team, but if she doesn't get a few kills , assist, or clears in, she will fall off in her ganks unless the opposing team is having a bad laning phase.
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Late game, it will just be as if she was playing mid-lane and will play as the clean-up after team fights
She has no resources, and great mobility so that can be a + I suppose. Despite all that, Katarina may be a lower tier jungler, but would be fun regardless. Of course, you may need specialized runes as well.