No you don't. Once you reach friendly with her you can fly up to the throne (before you get the quest inviting you up there) and buy it from the vendor. So... you only have to do about 60% of the quests instead of all of them. =x
60% of a zone I avoided intentionally... I hate my life. I don't understand why they didn't just make those enchants BOA. This will be my sixth time unlocking that stupid vendor.
I guess I'll have to pull my Priest through that place as well before she hits 85 (which will be in three more dungeons).
Another option is to just use the Wrath shoulder enchants. Those are BoA at least.
I agree though, it's stupid that the shoulders aren't BoA. The head enchants are in different zones at least, so depending on what kind of classes you have, you could potentially be able to do different zones to get them on everyone. Unless you're like me and level mostly casters of course.
The shoulder enchants all come from one zone, so it makes more sense to have them BoA so people don't get burnt out on Deepholm so badly.