Honestly, I think the only way "Azem" would have been part of Hydaelin's summoning is if Her Summoners made their own version of the Convocation and took on the titles of the members of the Convocation... but I don't see any practical reason to have done that outside of mockery, and from what little we saw of them they didn't seem the type to do something like that.

As for The Twelve being Azem and Friends... I mean... maybe? Wasn't it mentioned at some point that every so often a group of Brave Warriors show up and people think they're the Twelve reincarnated? While WoL = Azem = Azim/Azeyma IS an easy one. The rest of the Scions... I wouldn't bet on it...