Why go for a support like her when you have better options like Thresh (who can hook enemies at a distance, reposition an ally with his W, slow and damage with ult, and provide peel with his E) or Janna (armed with a kit to deny so many kills and provide good peeling).
What does an adc get with an Anivia support? Stunning the duo enemy laners with a q that she has to consistently land, a wall that can either screw the enemy team or screw your adc (which seems to happen most of the time imo), an E that mostly relies on her to land her Q, and an ult that she can't use effectively in lane (high mana-cost, not so beneficial until it fully forms, being careful to not use it on minions).
I'd argue that before the changes made to her a few months ago on her ult, she would be somewhat more viable as a support than she currently is. With that being said, I'd still take any other supports than her. If you wanna try something off-meta as a support, I'd play
. During the right opportunity, you can E onto the enemy, recast it, then root them with your W and ult them if your jungler is nearby for an good kill.