What's the survival rate for someone with carcinoid syndrome?

Depends: There are different grades of carcinoid. It also depends on the stage. However, most carcinoids are low grade and people can do well for several years even before starting therapy.

Quite long usually: Of all the variants of neuroendocrine cancer, carcinoid is usually very slow growing and we measure life expectancy in years to decades of life. This does not however mean that they do not produce quality of life limiting symptoms for patients with carcinoid syndrome. The syndrome can lead to malabsorption and its associated nutritional consequences as well as valvular disease of the heart.