Suppose the existence of objective morality is Turing unprovable, that means it exists so you'll never find a counterexample to show it doesn't but it also means you'll never find a proof (a demonstration in a finite number of steps) to show that it does. A moralist who designs a AI and gives the investigation of this problem priority over everything else will send the machine into a infinite loop. To make maters worse, you may not even be able to prove it's futile, that the issue is either false or true but unprovable, so I don't think it would be wise to hardwire a AI to keep working on any problem until an answer is found.
John K Clark