In the Netherlands it is largely frowned upon in palliative care, but a trial as complementary treatment could be conceivable. As an alternative treatment, replacing pain medication, it is hardly ethical, so that in my opinion is a definite No No. I don't know how things works in the US and Canada, but I imagine the sentiment would be the same. Homeopaths in the Netherlands have told some of their patients after they had already left the hospital that paracetamol is enough to kill the pain in combination with the homeopathic treatment. To say this to a slowly dying terminal patient in severe pain... Well, I think you can imagine what I what I would like to do (and I'm not just talking about the patient).
Actually, you just mentioned an illness that will clear up by itself and for which there is no treatment of the cause but only supportive treatment. So test away...
The timeline of the test needs argumentation, as would the reason to treat a patient.
The argument is, you need to show that there is a reason to test a drug on a patient. The reason (most often) could be that laboratory test showed a promising effect of the drug on animals or cell culture. Another reason could be that the drug was designed for another illness but has shown a promising effect that had not been recognized before. Yet another reason could be that many case reports led to a small patient group presenting beneficial effects of an formerly unknown substance. This has happened in the case of homeopathy, but the following trials failed to show a conclusive or even promising result under careful scrutiny by peers in the medical world. This normally means further research is shelved. But you don't start testing on patients first and analyze later. That is something you do in the lab on animals or cell culture. Even if the new drug is only a derivative of a already known drug, testing normally starts in the lab. I understand very well that you believe it is all bunk and they are only getting water anyway, so there would be no problem. But by subjecting patients to a trial, they have to follow the trial protocol. This means the patients are subjected to tests and a regimen that is often an infringement on the normal care given by their physician. For a benign problem (something you would encounter in a General Practitioner's office on a Monday morning) this can probably be done and the burden of the trial can be minimized. For more serious disease it becomes another story and I would have serious problems with the reasons for such a trial.
In general: A drug that does not work in the lab, does not make it to the patient.
( On a side note: I think some of the few exceptions where shortcuts were taken and testing in humans started long before labtests were finished were trials done by Bayer in WWII and more recently trials done on HIV patients in Africa, but I think we can agree this should not be considered normal )
SYL