Yes, it is possible that the inflammation of cytokine storms such as those caused by viruses like COVID-19 could lead to lingering post-viral depression and weight gain.
Cytokine storms are a type of overreaction of the immune system that can occur in response to a viral infection. During a cytokine storm, the body produces too many inflammatory cytokines, which can damage tissues and organs throughout the body.
There is some evidence that cytokine storms may contribute to post-viral depression and weight gain. For example, one study found that people who had experienced a cytokine storm during COVID-19 were more likely to experience depression and anxiety in the months following their infection. Another study found that people who had experienced a cytokine storm were more likely to experience weight gain in the months following their infection.