I tried various methods in Factions to bypass secondary, piggyback with quests on another character. I wasn't allowed into Minister Cho's, and not allowed leave for Seitung Harbor.
I believe only Nightfall characters can play most of the game without a secondary (anything but Nightfall).
During Dragon festival I think I will try get a Faction character without secondary to level 20. It's only possible with holiday quest spawns like Lesser Grasps. These are level 18 and fairly easy to kill. I questioned myself why, I still won't be able to leave newbie area

Only thing that changes is I'm allowed to get Kurzick/Luxon skills from Guild Hall but that's not why I would do it.