Could Harry have survived Avada Kedavra casted by a wizard other than Voldemort?

When Dumbledore tells Snape about Voldemort being held from death by the part of the soul attached to Harry, he then says that to be able to finish off Voldemort, the Dark Lord himself must kill Harry.

What was the point of this if Dumbledore could himself cast Avada Kedavra on Harry to remove part soul of Voldemort? Would it work? Or, would it only work if Voldemort himself killed Harry?