You can't move and attack at the same time. When you are chasing some one, you
move -> stop -> attack -> move (with stopping and attacking happening 'almost' simultaneous).
So if you would do more attacks, you would do more stops as well.
So would someone with, lets say 1.25 attack speed cover more distance then some one with 2.5 attack. If they contentiously attack and move when possible?
Best Answer
The movementspeed itself is obviously not influenced, except for Khalista.
What you are refering to is Orbwalking. You attack and break off the attack animation right after the damage is dealt/the projectile is flying.
The Attackframe is influenced by attackspeed (faster attacks = faster animation) So with higher attackspeed you can break the animation faster thus move farther with the same amount of attacks.
Note though that with faster AS you will get off more attacks in the same time which in turn reduce the distance you can move in a set time.