Gilard et al evaluated the diagnostic utility of the Adson test against electrophysiological studies, ultrasonography, helical computed tomography, and plain films. They reported a sensitivity of 79% and a specificity of 76% for the Adson test.

As with many clinical tests that is ok but not great news. It means 2 out of 10 patients who do have thoracic outlet syndrome you will miss with the test and likewise you will get about the same proportion of false positives. The way I would interpret that is that this can add weight to your clinical reasoning but you should also majorly take into account the history, particularly the symptoms that could be vascular in nature as well as other tests.

There is an alternative test: the hyperabduction test - diagnostic accuracy also reported in this study. With this test you can base it on symptom provocation or obliteration of a radial pulse. The accuracy was worse than Adsons particularly the specificity was very poor. However you could combine it with Adsons to try to lower the chance of false negatives with Adsons.

Gillard J, Perez-Cousin M, Hachulla E, et al. Diagnosing thoracic outlet syndrome: Contribution of provocative tests, ultrasonography,
electrophysiology, and helical computed tomography in 48 patients. Joint Bone Spine 2001;68:416-424.