No, it wouldn't, at all. People have been humiliating conspiracy theorists with the facts for decades, and the only result is that conspiracy theory has become mainstream. If all it took was a superior rational argument from an expert to convince people of the error of anti-vaxxers, there would be no anti-vaxxers. Yet even on HN, a forum that should be a nexus of rational thought, they dominate any thread where vaccines are a subject. The "sunlight is the best disinfectant" shit isn't working.
What will happen is exactly what people like RFK want to happen - their message will spread, the "experts" will be reframed and reedited and taken out of context through memes and bad-faith videos and exposes, and people will (as they always do) have sympathy for the "underdog" (the anti-vaxxers) and skepticism towards "experts" and wonder what they must be trying to hide.
This was also a huge loss for charity. The $3M could have helped a lot of people.