Would a complete patient profile blood test show cancer?

Maybe not. There is no standard "complete patient profile blood test" in the U.S., so what is tested for depends on what a doctor is looking for. A blood chemistry test such as a Comprehensive Metabolic Panel looks at 14-17 items, but isn't looking for cancer. It will, however, detect some side effects of having a widespread cancer problem. Cancers come in all sizes and many types, but need specific testing.