Rejoice, as you no longer need to do the questline to unlock Court of Stars/Arcway on alts, once you completed the dungeons on your main.
Reputation will not be made account-wide, no, but we will be easing a couple of linked features with 7.1.
First, Court of Stars and The Arcway will now unlock account-wide once each individual dungeon is completed once on an account.
Second, World Quests will no longer have the "friendly" reputation unlock requirement for secondary/alt characters. Once you hit 110 on an alt, you will immediately receive a quest to speak with Khadgar to receive your Flight Master's Whistle and unlock World Quests, as long as you've already unlocked World Quests on your main.