Does the cantrip Shillelagh and Hex Warrior class feature work together when you attack?

Question

If a Hexblade Warlock used the cantrip Shillelagh and attacked with a Quarterstaff would the class feature Hex Warrior and Shillelagh both apply to the attack and damage rolls?

Hex Warrior

When you attack with that weapon, you can use your Charisma modifier, instead of Strength or Dexterity, for the attack and damage rolls. This benefit lasts until you finish a long rest.

Shillelagh

For the duration, you can use your spellcasting ability instead of Strength for the attack and damage rolls of melee attacks using that weapon, and the weapon's damage die becomes a d8. The weapon also becomes magical, if it isn't already. The spell ends if you cast it again or if you let go of the weapon.

Answer 1

Yes, but the effects don't stack.

Hex Warrior says you "can use your Charisma... for the attack and damage rolls," while Shillelagh says you "can use your spellcasting ability... for the attack and damage rolls." Since the Warlock's spellcasting ability is Charisma, these both permit you to use your Charisma for the attack and damage rolls.

Though they both apply, the effects supersede each other. Neither rule says it adds anything like a bonus to the calculation, just that you can choose to use Charisma in place of the normal Strength or Dexterity modifiers used when making the attack and damage rolls. So they do both apply, but they do not stack or compound each other. The d8 effect of the Shillelagh would apply too.

So, you would be able to roll d20 + proficiency bonus + CHA for your attack roll and d8 + CHA for the damage roll, assuming you are proficient with the weapon and not accounting for any other effects that might also apply.