I have found that even if I get enough XP to level up a character during a quest, but still fail the quest, I do not get the reward that comes with that level up. It sill shows that you get the reward at the end of that game, but it never goes to the level up screen and instead jumps to the trading cards screen. I found this very annoying for a character that was in the high 20s and missed a skill bonus.
This bonus doesn't hold over for when you beat your next quest, it is just gone.