No, the Killing Curse, Avada Kedavra, would not work on a Horcrux. The purpose of a Horcrux is to protect a piece of the creator's soul from death. It acts as a safeguard, making it impervious to most forms of damage, including spells. In the Harry Potter series, it is mentioned that Horcruxes are highly resistant to destruction. They require specific means, such as basilisk venom or the sword of Gryffindor, to be destroyed. Regular spells, including Avada Kedavra, would not have any effect on a Horcrux. The idea behind Horcruxes is that they are intentionally made to be extremely difficult to destroy, as it ensures the creator's immortality and serves as a defense against their demise.