I have not seen any co-occurence statistics. As both lupus and rheumatoid arthritis are at about 1% (each), and many of them are taking HCQ, then if HCQ works[0] I would expect much fewer of them to be diagnosed with SARS-Cov-2 in the first place. This is something that the CDC _should_ be able to track, and doesn't even require any ethically questionable trials.

[0] and somehow the Lupus/RA mechanics are not influencing disease progress, which is not a trivial assumption, but does not disqualify the thought experiment entirely.