It usually works but Janna has OP disengage so you're gonna have a hard time sticking to either one of them even if you catch them in a stun. --- Going to church doesn't make you a Christian any more than standing in a garage makes you a car.
It's actually not that great, especially if the enemy support has some kind of heal in their kit. She provides next to nothing as a support except for a pretty fast, non-damaging, skill shot stun that's blocked by minions. She has no presence in a team fight and she just can't do anything without any items, which she'll be deprived of since she's supporting, and this is regardless of the fact that she has % based damage.
Edit: Forgot about her Volatile Spiderling, it can provide vision, which is amazing for what a champion can do, but only for a few seconds, which still isn't enough to play her as a support. --- The statement below is false. The statement above is true.