Such research happens all the time.
Search of: mdma - List Results - ClinicalTrials.gov or
Search of: PTSD | Canada - List Results - ClinicalTrials.gov
However, why doesn't the CAF/DND have such a "research centre"? Because the CAF is actually small potatoes, in terms of number of patients (potential patients) and the number of clinicians available to do dedicated research, though I'm sure some have been involved in clinical trials.
And though we have a "CBRN research centre" (I assume you're referring to Suffield), its focus is on defence and mitigation of NBC threats (oops sorry, my abbreviation is as dated as my involvement in trials there) and not with weapons development. And while I would not suggest that some chemical or biological substances that could be used as weapon precursors are not kept there, their use would be limited and does not extend to being tested on humans.