@ Jovy answered this question at length. This is what she wrote on the subject:
Quoted:
You can try her out for fun but I don't think she's really viable as a support. The only thing that would make her a possible support is that she has some sort of CC, but if that was all it took to be a strong support than practically any champion could be one; Cho, Elise, Xayah, Ashe etc.
RAMBLING ABOUT WHY SHE'D MAKE A BAD SUPPORT
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Zoe's strength comes from her burst, but if you play support you'll be giving up a lot of gold and at the very least delaying your damage by a long time since you won't be getting kills or CS. If you do build full damage, you still won't be as powerful during mid game when it is the most ideal time to be at your peak. Early-mid game enemies are still somewhat squishy whereas late game it's harder to pop them.
Some other issues are the length of the lane. I've heard my friend complain about using her E because the lane is so much longer than mid lane and without using walls Es range is thus noticeably smaller/less effective.
Then unless you take the odd minion from your ADC, you won't be able to use your W as effectively as well.
When Zoe came out and I rushed her to get level 5 mastery I played mostly mid or support when some1 choosed mid lane. She's a good support but I would still recommend building her as typical mid laner with AP items. Also you suppose to take E first and first item should be support ne to get more gold.
I would recommend trying it out with ADCs like Jhin or Jinx due to their own form of cc that can make up for the cooldown on your Sleepy Trouble Bubble. Try it out in a normal game,and it may be very fun to play!
Zoe could technically be a support, but very situationally. Ive seen her work well with adc's that can blow up a single champ, something like a Draven.
RAMBLING ABOUT WHY SHE'D MAKE A BAD SUPPORT
I would recommend trying it out with ADCs like Jhin or Jinx due to their own form of cc that can make up for the cooldown on your Sleepy Trouble Bubble. Try it out in a normal game,and it may be very fun to play!
Zoe could technically be a support, but very situationally. Ive seen her work well with adc's that can blow up a single champ, something like a Draven.
Hope this Helps,
~moon