Preists have an equal questline, but it does not have them go into the old Onyxia like the Hunter quest did. Blizz used Hunters and Priests as a test bed to try some epic quests for each class but ended up abandoning the project. This kind of sucks since the sinew is like a 100% drop rate now. At level 60 I remember running Onyxia raid every week for like 4 months waiting for it to drop.
It is interesting that you get the feat of strength achievment
Onyxia lvl 60 for this. It doesn't count towards achievment points it is just a bragging achievment.