No, as others have said it has no impact on the speed at which your attacks or skills fire. Speed can indirectly lead to dealing more damage though. In the right hands, speed is the defense, so the player can solely focus on offense.
If I’m dancing around you on my wild hunt speedcro, and you’re struggling to target or hit me, I’m not having to block, break free, cleanse or heal. That means my time and resources are fully dedicated to killing you.