I am leaning towards the opposite conclusion based on three things I have heard.

I have heard vitamin D described as a "modulator for the immune system" (isn't the problem with Covid that your immune system is overreacting?). Also I know that its a factor in Multiple Sclerosis, which is an autoimmune disease. Also things like flu infect / kill more people in winter- when people will be getting less sun, and so have less vitamin D.