Will a complete blood count show signs of having cancer?

Not a test for. Cancer. With the exception of some leukemias, complete blood count is not likely to reveal the presence of cancer.

Related Questions

Can a complete blood count test diagnose leukemia or other cancers?

Sometimes. Most leukemia have an abnormal CBC that will at least raise the suspicion of leukemia; leukemic cells in the blood are often sufficient to make the initial call; when leukemia is confined to the marrow ("aleukemic leukemia"), there are usually some suggstive CBC abnormalities. Most other cancers can't be spotted on the CBC and even in the advanced stages the CBC is often normal.
Usually leukemia. A CBC with differential can detect features worrisome for a leukemia (high or low white count, anemia, or thrombocytopenia). The automated machine can detect abnormal cells which flags for a technologist and/or pathologist to manually identify and count under the microscope. Then a flow cytometry test may be done to determine the lineage of the cells for the actual type of leukemia.