Paul Farquhar
Legend
It doesn't.In fact, it may be possible to get a discount Two Weapon Fighting Style if Hex Warrior gives you charisma to damage on your off-hand.
It lets you use charisma instead of Strength or Dex. If you don't get a strength or dex bonus you can't get a cha bonus.
If you multiclass to fighter and get two weapon fighting style, then you can dual wield and apply your cha bonus to your off hand weapon, but not without.