I suspect this is going to pull in two directions.

On the one hand, people are already developing some level of warning label fatigue, where they skim over the labels without registering the content just like they do on-line ads. (Both practices are doubtless known to cause cancer in California.)

On the other hand, there's a type of personality who may, in fact, change their minds about buying if presented with a short, sharp "this is bad for you" reminder on the way to the checkout.

Putting the labels on is, overall, a harmless experiment to try, so we might as well see if it does any good. Personally, I don't think we're going to see much change until we spend a couple of decades broadcasting and reinforcing the "no amount is safe" message, and even then many people will keep drinking. Just as there are still smokers today, even after many decades of "you will die horribly if you do this" messaging.