Syndra has decent peel against one-off engagers (pre-6 leona, pre-6 nautilus). Unfortunately, her mana pool isn't durable enough versus the likes of Janna or Soraka and she's mostly a damage dealer, so going support will mean you'll do subpar damage and CC.
I believe she could be decent with a good mana regen item and a rilay's as far as peeling go, provided you can hit your spells. However, getting the gold for these items won't be easy
Metas shift frequently in League, so it's hard to pinpoint if something were to be viable or not. Maybe in certain situations. Like as in Nautilus support just gained a huge spike in popularity as in s4, he wasn't even considered a support. Morganna was made to be a mid-laner, but now she's mostly support. So needless to say, you can't really answer that question. A better question would be how good syndra does against other supports. and my answer would be she does ok in certain situations, like against Braum or an immobile ADC like Kogmaw.
It theoretically could work, because she can slow her opponents if she's able to hit them with a minion, and if she builds AP she could possibly be the next support similar to Annie, but I wouldn't recommend trying it in ranked until you're fairly certain it's possible, if it does work, inform me, because this does sound fairly interesting.
I believe she could be decent with a good mana regen item and a rilay's as far as peeling go, provided you can hit your spells. However, getting the gold for these items won't be easy