I say that it is not. Jesus said that one should not test God [Matthew 4:7] and when tested Him by asking whether he would produce a miraculous sign, he refused to do so. [Matthew 16:1-4] In a relationship where testing occurs, it is typically a one-way relationship between the one who does the testing and the one who gets tested. In calculus class I test my students; they do not test me. When I go the DMV to get my driver's license, they test my eyesight and hearing; I do not test them. In both cases there's an authority figure who gives a test to a supplicant. Likewise God is our authority figure and we are the supplicants. For people to test God would represent an inversion of the Christian understanding about the relationship between God and humanity.
Here's an analogy that I've often used before. Imagine I say that my mother is willing to bake a cake for me, and someone insists on putting the claim to an experimental test. Five hundred subjects will be randomly assigned to two groups, A and B. Those in group A will ask my mother to bake them a cake, while those in group B will not. Then we will count how many members of each group receive a cake from my mother. What would the result be? Presumably no member of either group would receive a cake from my mother, because the experiment by nature is insulting to her, and there's no logical reason for her to participate in it.
Even if we removed the particular difficulty that the Christian God is an authority figure who cannot be tested, I don't see how prayer could be tested even for a generic deity of any religion. When we do an experiment, we apply a treatment to one group of things, but not to a control group. For example, we might give fertilizer to one group of pea plants but not to another. Then we'd observe the growth of both groups and compare to determine what effect the fertilizer had. But such an experiment is based on the assumption that the pea plants don't know what's going on and can't take an action just because they feel like it. If we instead had somebody pray to God for the growth of the pea plants in one group but not the other, God could very well decide to augment the growth of the plants in both groups, because God is an intelligent being. Hence the final result would not necessarily tell us anything about the effects of prayer on the growth of pea plants.