No, not reliable for coyotes. Fox should be OK.
If I'm going to attempt to kill the animal, I want a clean, quick kill.
I've never owned a 17HMR, nor even shot one. My conclusion is based on many dozens of coyotes killed with my 22 Hornet, which is way more powerful than the 17HMR, with twice the bullet weight (45gr) and 10% more speed (2,875fps).
With the Hornet, my limit is about 100yds if they are facing me (typical calling situation) to about 150-175 if they are broadside.