If I had a weak immune system would my CBC test show it?

Not necessarily. A complete blood count only looks at white blood cells, red blood cells and platelets. The immune system can become compromised with a myriad of conditions (diabetes for example - where the CBC is often normal) speak to your physician why you think your immune system is compromised and go from there. In the meantime do not forget that food is medicine. Eat healthy, exercise, get adequate sleep.