Is the South Korean national anthem played before all Tae Kwon Do events?

Not at all Taekwondo events in every country of the world, but it is a common practice among those events (tournaments) that are run by Korean Masters, or have prominent Koreans or Grandmasters present as honored guests.

Naturally, the South Korean anthem would be played at Taekwondo events in South Korea, but in other countries, it is up to the host of the event. Typically, the national anthem of the host country is played, and the South Korean anthem might be played as well to show respect and honor to the country where Taekwondo was born. Keep in mind, that versions of Taekwondo (particularly from one splinter of the ITF) are taught in North Korea, where the South Korean anthem is most likely not played.