Hi,
No. They only do something when used. For example, if you set a Dialogue System Trigger to OnUse, it will only do something when you send an OnUse message to it. If you set a Dialogue System Trigger to OnTriggerEnter, it must have a trigger collider, which does require a little processing by the physics engine.
But that's just physics, nothing specific to the Dialogue System. The Dialogue System does provide a helper component called Range Trigger. You can add a big trigger to an area, and add a Range Trigger. Then configure the GameObjects and/or components that should be active when inside the Range Trigger.
For example, say your scene is a neighborhood with a theater and a restaurant. You have Dialogue System Triggers inside both. When the player is inside the theater, there is no need for the physics engine to keep track of the trigger colliders inside the restaurant, so you can keep the restaurant's triggers inactive. You can add a Range Trigger to the restaurant that reactivates them when the player enters the restaurant.