She can. She's a lot like Rammus where she basically can't clear the jungle after a certain point, so she's really reliant on getting kills or global gold early on. Also, her clear speed is ass.
Your build is weird as shit, tho. She's not bursty enough to use the triforce->shiv build, Hydra is a really bad item on her in almost all cases, and Merc Scimitar is only good against Malzahar et al. Also, Ignite over Flash is awful on pretty much everyone except Shaco and maybe Eve.
There are basically three builds that I've had success with. In order of preference -

Running 9/0/21 with 5% CDR from Runes, and maxing E. This build will ultimately give you a 2 second point and click stun on a 4.something second cooldown at around 15 minutes, which is really fucking powerful. You can pick off isolated targets or peel for your carries really well, and you scale pretty nicely into the late game with the bonus HP from golem. If you aren't ahead, just by a Sheen and go straight into tank items - the full Triforce is a pretty snowbally item.I like this build because it lets her bring something that very few other junglers have (point and click hard CC on a low cooldown).

Running 21/9/0 with AD/AS Runes, maxing either Q or W. Basically a standard assassin jungler build - leap on somebody, ult them in the face, hope they die. This build isn't bad, but I think it's pretty hard to justify taking Irelia over someone like Rengar if you want an AD assassin jungler. I mention maxing Q as an option because A) It's her only source of Physical damage outside of auto attacks, and B) It lets you get resets on your Q when you jump to a caster minion, which is pretty important.

Feral Flare is awkward on Irelia because she's actually really bad at farming the jungle, even tho it has synergy with her Q and W. I honestly don't think there's ever a situation where this is a better choice than just playing Master Yi, but it can be kinda fun if you get really far ahead.