It doesn't really help that much.
Especially since when most people say chicken noodle, they mean soup from a can with a red label.
There are virtually no truly valuable nutrients in chicken stock. What chicken stock does have, though, is an asston of salt content.
The salt is soothing on the throat and can help open your sinuses a tiny bit (when you breath in the salty steam as you drink it/put your face over the bowl). Other than that, I really don't think there's much immune system boosting going on at all. There are MUCH more nutritious foods to eat--even if the soup is homemade with high quality ingredients.