The Gun-Fu perk at the top of the agility tree sounds great.
Notably however, other than the name and flavor text, the actual perk text makes no specific reference to guns:
Rank 1: You’ve learned to apply ancient martial arts to gunplay! Do 25% more damage to your second V.A.T.S. target and beyond. (Requires: AGL 10).
Rank 2: In V.A.T.S. you do 50% more damage to your third target and beyond. (Requires: Level 26, AGL 10).
Rank 3: In V.A.T.S. you instantly do a Critical Hit against your fourth target and beyond. (Requires: Level 50, AGL 10)
Compare that to the text of just about every other perk, which specifically calls out what weapons it affects, or it affects all of them.
Does Gun-Fu work with melee weapons?
No, it doesn’t appear to do so. I tested both unarmed and with a pool cue against a group of six ghouls putting one hit on each and did the same damage to each of them.
Other players have tested this, too and can verify that the Gun-Fu perk doesn’t affect melee weapons.