It is far different from Brand/Annie/Vel'Koz support.
Brand and Vel'Koz have passive that give them a lot of free % health damage without the need for levels or items. Zyra, another mage support, just have super high base damage due to her plants.
Annie has higher attack range than the majority of ADCs and supports, this is the main reason why she is actually viable as a support, because she has high base harass in early game due to her auto attacks setting her danger zone higher than the enemy, reducing her dependence to level and items in the early game. Losing your lane as an Annie support is pretty much making you completely worthless for the rest of the game however.
Leblanc doesn't have either of those. She scales on levels and items. A support is almost always going to be the lowest level on their team and without the base damage from Leblanc spells and no items for her scaling, her damage will absolutely not be dangerous against any competent bot lane.
I've played my share of mage support in normals, I don't play them in ranked because I'd rather stick with a style I am more familiar with and when I need AP damage, I go for Sona instead.
I've fought all sort of support, even saw someone try to play Vayne support. I'm not talking out of my ass when I'm saying Leblanc wouldn't be a good support. You can support with any champion and win, doesn't make them good at support, just means you won your game. There are a thousand reasons why you would win a game.
I've got Mastery 7 on Taliyah from playing Support Taliyah in normals. Doesn't mean I consider Taliyah to be good as a Support. Taliyah is too dependent on getting an early Rylai and suffer from her scaling if she goes support.
And regarding the whole "Burst the ADC". It does take a lot to burst an ADC in bot lane when you aren't snowballing. The ADC has Summoner Heal and the enemy support is usually carrying around Exhaust or has defensive abilities like shields, heals or other ways to prevent damage done to its ADC.
It is actually MUCH harder to kill an opponent in a two-man lane than in a one-man lane. Because in a two man lane, you always have to put yourself in danger when trying to engage. And let's just say that... a Leblanc isn't exactly the hardest thing to kill. If you dash in to attack, you may find yourself pinned to a wall by a Vayne, stunned by a Leona or simply bursted down by a Caliber net and a Power Chord Q.