If it can truly be tested, then it should be tested! But how do you truly test it? Even if God isn't real, acts like prayer give you emotional support and that can have a very real effect! So if you merely want to test whether an act like prayer is effective, then that's simple and probably already done and also probably shows some effect. However if you want to prove that prayer in a particular method to a particular God is effective, that's tricky. If someone can design an elegant enough study then it should be tested!
Ok, that would address the unethical part, but still, does that sound like a good use of limit research dollars?
This is one of those instances where judgement is a good thing. Don’t run such a silly trial. Spend the money on something that actually has a chance to work.