Unfortunately, my sense is that it will be close to the complete opposite: the mainstream narrative going forward will be that the vaccines worked - that lockdowns, physical distancing, and masks helped a bit, but it was mostly the vaccines. This will be a dominant narrative for quite a while, and will justify future "booster shots," and perhaps more sophisticated vaccine experiments on the human population in real time for years to come.
Those who dutifully followed the mask mandates, physical distancing, lockdown impositions, and got all 2+ of their vaccine jabs will congratulate themselves on "beating the invisible enemy," and henceforth may condescendingly look down on the minority that did not, and say that herd immunity was achieved through vaccines.
The masses will believe they saved themselves - as well as the cv19 "conspiracy theorists" - through their abject obedience to government regulations.