Does an ordinary urinalysis and blood test for hiv and syphilis test/show/detect pregnancy?

No: No Both the urine and blood test must specifically be ordered for the hormone human chorionic gonadotropin (hCG) which tests for pregnancy.

Not automatically: Either fluid can be tested for pregnancy but each test requires separate lab materials, time and expense. These tests are not automatically done by the test wizard, they must be ordered and eventually paid for by some entity. If you are worried you may be pregnant you can do a urine pregnancy test at home. They are available OTC at low cost.