Well, I guess it's just an empirical question where we differ in predictions. Personally I don't think the analogy with public speaking is very strong, because public speaking classes are actually public speaking. People stand up and speak in front of lots of people, that's just what it is.

Upon reflection though, it does seem like there's one way that it might help, which is that it might help you figure out how to go about non-conformity, what exactly you can do or say in such a situation. So even if your mind doesn't buy into the charade, roleplaying with good partners might help you figure out ways to navigate a non-conformity situation. Having those methods worked out in advance might make you less hesitant to speak out in real world situations, but only to the extent that your hesitation is about not knowing what exactly to say or do (as opposed to fear of social punishment, the usual explanation for Asch's results).

What I've always wondered about with Asch's experiment is how much of a difference a small monetary incentive (say, $1 per correct answer) would make. It seems like the experiment is odd in that there is no incentive to give correct answers, but at least a potential or perceived social incentive to give conforming ones. This seems like it would be relevant to our disagreement because it's a question of whether the situation becomes different when something is actually on the line. Unfortunately I can't seem to google up any examples of variations like this.