Literally nothing about the Legion expansion's main storyline is tied to the order halls. You can level your character all the way to level 60 in the Broken Isles without ever setting foot in the order halls and not miss any part of the main storyline. The order halls are unnecessary to the leveling experience.
Even when the Legion expansion was the current expansion you could go all the way to max level without touching your order halls. You could just literally head into any of the zones and start questing there.