I have no idea. The immune system is so complex that it's not a one size fits all situation.
In theory, cancer can be caused because the immune system does not recognize a cancer cell as a 'bad cell', so it doesn't try to or cannot destroy it. Immunosuppressants can actually raise the cancer risk, because they cause the immune system to not function fully or adequately, and those cells can slip by and grow. You'd want a strong immune system to fight cancer.
Immunosuppressants can work for autoimmune disorders though, so the reverse seems to be true.
It's complicated. I guess all you can do is try the mushrooms if you happen to like them.