John,
Not a stupid question! I have not experienced as many colds since my neck dissection, but I think it has more to do with scrupulous hand washing than anything else. I do get a flu shot every year and am considered "high risk" for flu due to history of cancer. (Get them free from employer and when the vaccine is scarce, that is why I was allowed a shot.)
Hope that helps!
Sincerely,
Lisa