Okay, it would probably would trigger the "Don't ask for signs and wonders" clause (John 4.48), and for this reason I'm sure some Christians would refuse to take part in the experiment. (Genuine Christians would be needed, because of course the prayers would have to be sincere to count.) On the other hand, while it's meant to be very vulgar to ask for signs as a way of inducing belief, the Evangelists did in fact record the details of many signs and wonders in the Gospels, presumably with the intention of persuading their readers of Jesus's bona fides, and many evangelical preachers in particular use public prayers in faith-healing for the same purpose in their churches every week of the year, so I don't think the objection can be a very strong one. (I know too that many Christians believe that prayer is more about reconciliation with the will of God than about asking him to do something he wouldn't otherwise have done; obviously my experiment would involve the other kind.)
My brother and I once got our father (a convinced dowser) to try to tell the difference between Coke and Pepsi by means of his trusty pendulum alone. It was not a great success, partly because our dubiety played havoc with the subtle energy fields needed for the task. Experimental design is obviously important in this kind of exercise, and for this reason I suggest that everyone involved ought to be a Christian, or at least an agnostic, so as to insulate the process against scepticism. Probably other faith groups should be excluded on the same basis, on the understanding that their prayers (where applicable) can be tested separately at a later date.