Relic Shield on support Annie

ap and mana regen is what you need. so no

Annie doesn't need the health. She would rather the AP and mana regen.

I have seen tank annie work in aram, but I don't think it would be good in an SR game.

Getting AP and bursting your targets is just a more straightfoward way to succeed on annie. If you really want to, you can probably make that work, especially in lower elos. That doesn't mean it's good, though.