Can an abcessed tooth poison my body?

Spread to your brain. One problem is that the infection can easily spread along nerves and blood vessels. From the mouth there is ready access to the brain and other sensitive structures. It is thought that king tut died of an oral abscess that spread to his brain. Don't delay, see you doc right away!
Yes. An abscess is simply a collection of white blood cells fighting bacteria or other types of microorganisms. If the white blood cells are unable to get the infection under control, the bacteria may then "escape" into the blood stream. This is what is referred to as blood poisoning health professionals call this sepsis and a tooth abscess can cause this. (see left lower jaw abscess on ct).
Yes. Untreated tooth abscesses carry the risk for generalized infections, and in the worst case heart valve infections or septic shock. Fortunately, most tooth infections don't end up this way, but it is one reason (along with the pain!) that prompt therapy is warranted. See a dentist asap.