Is there a test that can detect blood poisoning from abscessed teeth?

A blood sample. "blood poisoning" usually is taken to mean bacteria in the blood, or bacteremia. You can take a sample of the blood and culture it to see if bacteria grow. There are many infections, including teeth infections, that can cause bacteria to go into the blood.
Yes. "blood poisoning" would usually mean that there is bacteria in the blood. Blood tests can be performed that measure the number of white blood cells - elevated white blood cells is an indication of an infection. Bacteria in blood can be stained with specialized stains and be seen on a slide under a microscope and the blood can be cultured to identify bacteria.