If I were to meet someone with the pneumonic plague, could I catch it?

Yes. The plague is usually bubonic (one catches it from being bit by infected fleas or rodents, and the bacteria infects one's lymph nodes) or pneumonic (one catches it by breathing infected moisture droplets exhaled, sneezed, or coughed out by an infected person or animal, and the bacteria infects one's lungs). Without treatment, pneumonic plague is fatal.