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 Fischietto del Maestro di Volo
and unlock World Quests, as long as you've already unlocked World Quests on your main.
Hope this answers your concerns! :)