If you roleplayed a Hunter under a Beast Master archetype, someone whose expertise is in hunting and taming the wildest and most dangerous beast on Azeroth.
Would having a pet Storm Wolf (think like Hati, BUT NOT Hati itself.) Be a little lore breaking? You can tame them in game.
*As the Champion of Azeroth standin. Keep in mind that not everything we do in-game is indicative of plausibility for someone who isn’t the Mary Sue PC.
Having said that it wouldn’t be impossible under the right circumstances. Hati isn’t the only “storm wolf” in existence, and we have plenty of other examples of Elementally-inclined animals (such as the Lava Spiders, both big and small).
I’d figure someone incredibly in tune to the more primal nature of hunting, or even someone with more Shamanistic inclinations due to personal belief/culture would be fine having a storm wolf.
You can also use models as standins for custom pets and characters - Hati doesn’t have to be “Hati”.
For some reason I was convinced this thread was about the WH40k Storm Wolves (descendant of Space Wolves).
I’m not entirely sure, personally.
I’ve kept a close eye on all things hunters when it comes to recent lore ever since the Unseen Path. Thorim’s story is very strange, but super indicative that he has either made several storm wolves, or that his brother has, or that Mimirion has as well.
One key thing to keep in mind, however, was that Northrend was a giant love letter for Chris Metzen and Samwise’s love for Norse mythology. Hati and Skoll were two wolves that chased the sun and moon to bring about Ragnarok.
As these beings are basically demigods, along with most spirit beasts, I can’t say that storm wolves in character are necessarily canon, or, lore friendly. I’d give a longer explanation, but most BM hunters probably agree. WoW-Skoll was/is evil, and we only cared and loved Hati so much because in Legion the 10 year fantasy of “can we pls have more than one pet out” was fulfilled. 
There are generic unnamed storm wolves running around the Vale of Eternal Blossoms and Zuldazar.
I don’t see a problem with using Hati to represent one of these.
Wow. I completely forgot about the ones in the Vale.
I feel stupid.