I would argue that's exactly what it does.
I'd further argue that hate speech and the threat of violence should be separated into two distinct categories for clarity. Clarity is extremely, extremely important when you're dealing with the edges of acceptable speech. It's dangerous to load them both into one concept that can be wielded by politicians and the media for control purposes over speech and free expression.
It's also important to clarify that the threat of violence is not a form of speech, it's a threat (of violence). That's another obvious reason why "hate speech" should not cover threats of violence to begin with, it intentionally muddles the concepts. Just like smashing someone in the face should not fall under free expression: it's an act of violence. Free speech ends at the point of violence, putting violence and speech together generates a contradiction of terms that can only benefit people looking for levers of control.
The concept "hate speech" is already a broken, frequently abused tool for controlling people. It's clearly going to get much worse in the coming years given the rise of extreme political correctness, the 'protect my feelings' movement. "Hate speech" is by default devoid of nearly all meaning, and nearly anything can be claimed to be hate speech, because "hate" is a generic term that can vary wildly and is inherently subjective. It was of course used for that exact reason: you can't legislate control over speech, therefore create empty jargon to do the same thing, and then load anything you want into it. A method frequently employed by totalitarian regimes.
Are my posts, which openly express my dislike of elves, hate speech? You bet. Why? Because I say so. You can never successfully refute that.