Mildly interesting, but it's too easy to see how this plays out. Theists will say that this test is not valid for any number of reasons-- you can't put god to the test like this, you can't test the supernatural scientifically, and so on. But if any research showed even a non-significant statistical correlation between prayer and recovery, they'd be all over it as "proof that prayer works!!!"
"Well, evolution is a theory. It is also a fact. And facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts don't go away when scientists debate rival theories to explain them. Einstein's theory of gravitation replaced Newton's in this century, but apples didn't suspend themselves in midair, pending the outcome. And humans evolved from ape- like ancestors whether they did so by Darwin's proposed mechanism or by some other yet to be discovered."
-Stephen Jay Gould
-Stephen Jay Gould