Yes that is a serious experiment.
As I understand it, when the original article was published there was a huge uproar in the academic community about the findings and intentions of the study. Those concerns were addressed in a reply from the author:
"The purpose of the article was to ask the following question: Would you believe in a study that looks methodologically correct but tests something that is completely out of people's frame (or model) of the physical world---for example, retroactive intervention or badly distilled water for asthma?
There are three ways to deal with this question:
(1) To answer in the affirmative. But this leads to such paradoxes (some described by those who responded to this article1) that it is incompatible with scientific work or even daily life.
(2) To look for methodological or statistical faults. Here an obvious one was that the duration of fever and the duration of hospital stay are related. But what if the next study sports perfect methodology and statistics?
(3) To deny from the beginning that empirical methods can be applied to questions that are completely outside the scientific model of the physical world. Or in a more formal way, if the pre-trial probability is infinitesimally low, the results of the trial will not really change it, and the trial should not be performed. This, to my mind, turns the article into a non-study, although the details provided in the publication (randomisation done only once, statement of a wish, analysis, etc) are correct.
The article has nothing to do with religion. I believe that prayer is a real comfort and help to a believer. I do not believe it should be tested in controlled trials."
"Evidence based" has recently become a popular ideology/buzzword in the medical community. Although it is always comforting to have a tangible set of numbers to reference, "evidence-based" findings are often adopted without legitimate consideration of experience-based/anecdotal data.
It is the current culture to accept anything with the label of science as indisputable truth. As a rule, I don't think it is ever a good idea to blindly follow. Even the most well designed studies are worth debating. The more you question, the more you discover.