Chopra and colleagues have published a case report of a Long COVID patient getting better after MDMA and Psilocybin. This made me take a deeper look into survey data that I collected. While I didn’t ask about MDMA, at least 7% of the patients surveyed tried psychedelic mushrooms. Or 51 people.
None of the recovered patients rated these as leading to significant improvement (not shown above but you can find the data here). 
This intervention also carries some risk.
The bottom line
So it doesn’t look like the greatest treatment out there.
Here’s the case report in case you’re interested: