I've seen some posts about this on battle.net and some people say yes and others say no. I haven't found a blue post about this to confirm either of those opinions.
Since the Suramar mythic dungeons were not initially account-wide when opened you had to quest through Suramar with every character in order to get in, which Blizzard patched later to require this step only once.
Does this now apply for Karazhan as well or do you have to quest again with every single toon you want to get into the dungeon with (and Blizzard making it account-wide later again)?
Best Answer
Yes, it is account wide.
Source: I just tested it with my alt, who has not done the attunement.