In answering this question there's a necessity to be precise with terminology, because otherwise "yes," "no," and "what the heck do you mean?" are all valid answers.
In the chemistry sense: Vanillin does not contain alcohol, it is an alcohol; that is, it's an organic compound with an -OH group.
In the normal person sense: Vanillin itself does not contain alcohol, but vanilla extract does usually contain alcohol; again, to be specific, it usually contains ethyl alcohol, which is what most non-chemists mean when they say "alcohol."