Not so much, actually.
Most people leveling do it alone or maybe in a small group. No need to think about 90% of the abilities a class has while doing that because the leveling content needs to be tuned to people who are novices. Most people don't want - despite playing an MMO - to be forced to play with other people in a group at all times in order to level, so you can't touch this leveling content.
Most people leveling don't even set foot in a dungeon in WoW. A dungeon being fundamentally different than world questing, and yet still not requiring a player to be very good with their class or understand their class.
A tiny percentage of players set foot in a raid EVER, let alone while leveling - even with new things like a very content-tourist mode like the Looking for Raid feature that was added. Raid mechanics are fundamentally different than dungeons or world questing, so really, require you to play your class in a very different way than you would have experienced while leveling; abilities that seem pointless while leveling suddenly make sense to use, and patterns that made sense while leveling suddenly become counter to survival.
What IS true is that, if you want to raid you need to learn how to play your class. But, I don't think 20-100 hours of doing things that bear no real relation to how you will end up playing your class is the way to do it. Personally, I think the idea of having proving grounds (which they kind of do now) wherein the player is hand held by NPCs and given tons of feedback on how to play their specific class, what abilities to use and why, in game, would be the way to go.
"Hey, new paladin person in a tank role - I'm going to make that big guy over there very, very angry in a moment, and he can kill me but he won't hurt you as much, so I want you to press that flashing button on your screen - it's called a taunt - when he starts chasing me; it'll make him go after you, not me!" If you fail? "It's okay, fortunately we have people around who can make everything better when I get beaten to a pulp... Let's try this again..."
"Hey, priest type person in a healer role - I'm about to fight several small creatures that individually don't do much to me but hurt me slowly over time. Cast that spell that's flashing on me once every 10 seconds or so in order to throw a spell on me that will heal me up slowly over time."
"Hey, shooty damage type person, I'm going to beat up 4 things, but I want you to focus on hurting ONLY the one that is my primary target." "Hey, so these guys aren't stupid, they're going to try to hurt you - see that purple stuff on the floor over there? If it appears under you during the fight, MOVE AWAY FROM IT!"
Etc. and so on. Have people go through that, have it be so that a veteran player who is familiar with game mechanics could complete all the tasks in under an hour, but where a newbie player who knows nothing might wind up taking 10 hours or so to do the quests well enough, and you're good.
The problem WoW has - and most MMO's have - is that the designers assumed that other players would give solid feedback to people on their teams in dungeons and so on. Unfortunately, most people are assholes and not willing to take any time with newbies to straighten them out. Since the playerbase by and large won't help other people learn, there needs to be an in game process for it.
tl;dr: There needs to be a way to teach people how to play their class, but the current way of doing it (leveling) doesn't teach them anything that is actually relevant.