I don't believe I'd use a .17 HMR on small game I'd like to eat. Those little bullets come apart pretty easily and I don't want to pick bullet jacket out of my teeth. I don't think I'd shoot a deer with one either, it just doesn't seem right.
I've seen the .22LR used on deer and if you get close and place your bullet, it does okay. They penetrate well, and those little bullets would get into the vitals.
However, having said that, one of the reality shows, Swamp People, show Jay Paul Molinere killing alligators with the .17 HMR. I don't know that I'd use that caliber for alligator, preferring to use a larger centerfire. The few gators I've had to shoot have seemed a lot tougher than the .17 caliber, yet I watch that young man kill them with a .17 almost every week. Disclaimer: I'm not an alligator fisherman, but I live in Louisiana. I've had to kill gators for self-defense, and defense of livestock. I like to eat gator, but I don't like skinning them.