I wouldn't do a thyroid test run without the full panel results to support the need for it.
My previous vet told me that nothing bad could happen to my non-greyhound by running a drug trial on him.
My new vet thinks that it is very likely that the medication contributed to the series of strokes that he had, since he was not hypothyroid, but had cancer.
I can't remember the lab, (MSU?) that runs the full thyroid panel-but if you need that information for your vet, I'm sure another GTer will chime in with it, or I can look it up when I get home.
I had a bad experience, and am a little jaded-but there can be bad side effects with ANY drug. Vets tell us that Rimadyl is completely safe, and yet there are dogs that have passed from adverse reactions to it as well. Again, the cases that I know about had contributing undiagnosed health issues, but it has happened.
I'm not saying that your dog is not hypothyroid or that he doesn't need medication-I'm just saying that I personally would make sure that the need is there before doing a "trial."