Ads do work, yes. But not because they present true facts. It's because people tend to buy things that are from brands that they remember (a form of recency bias I guess, although not sure about that). So if you know nothing about which ice cream brand is best, you'll default to the one that had an ad saying "We sell ice cream!". That's, again, a well-studied effect. Consumers are not rational.

I don't remember seeing many tv commercials with a comparison table containing technical specs.