For HIV testing, the only immune suppression treatment that might have any effect on reliable results would require very high doses of very potent drugs, of the sort
used in cancer chemotherapy and
for other life-threatening conditions. And even this is theoretical only, with no reported cases (to my knowledge) that it actually happened.
So all that is in response to the title of your question. Now that I have read the res, I think you'll agree I already nailed it.