When completely bare-handed (no weapon equipped), swings will still be at a normal speed and unaffected by this perk.
This perk does not affect Action Point costs. However, the increased speed does make V.A.T.S. attacks execute faster, thus reducing the amount of time that the Courier is "locked" in V.A.T.S. sequences where they are left vulnerable.
The benefit of this perk can be utilized even more with the consumption of rushing water, offering a combination of +80% Melee/Unarmed attack speed.