So, with the TRUST system I never have to wait to queue for a dungeon in ShB?

[Xtrasweettea]

[…]I am also wondering how it impacts queue times. Will most people opt to bypass the Duty Finder and go with TRUST, significantly extending wait times or will it have the opposite impact and reduce them?

It would more-than-likely do nothing to queue times over the long run. The Trust System isn’t just for DPS, it is also available for Tanks and Healers to use. Even though Tanks and Healers on average have near instant queues, there will be those who do not want to deal with real people and will opt to just use the trust system.