Could doctors tell if you have leukemia by a blood test?

Yes, most times: Most leukemias will show up in blood sooner or later although they start in the bone marrow to begin with. So a blood test will show some abnormalities either in hb, WBC or platelet counts. The most critical change of course is abnormal WBC and presence of leukemia cells(blasts) in the peripheral blood.

More and more....: The answer is yes, as highly sensitive flow cytometers can identify even small quantities of circulating leukemia cells. However, some leukemias are dominated by marrow infiltration without significant circulating leukemic burden. For these patients, a bone marrow aspiration and biopsy can confirm the diagnosis and establish phenotype. In truth bone marrow eval is done in most cases.

Usually yes: If there are signs and symptoms suspicious of leukemia, the initial test is usually a blood test (cbc with differential and morphology) followed by a bone marrow study.