We won't know for a while how much influence Vance has, and even then we probably won't be able to say with any certainty. But he and Trump are almost certainly right. The choice of vice president doesn't matter. And the choices that people thought mattered didn't actually matter. Sarah Palin was a bad choice in 2008, and got significantly worse after the housing crisis began. Joe Biden, on the other hand, was a good choice. But neither changed the course of the race. There's little evidence that vice presidents change votes in their home states, much less nationally. Vance may be a bit creepy, and he certainly draws attention to Trump's poor judgment, advanced age, and general extremism, but voters already know that Trump is old, extremist, and pretty nuts.
Moreover, one of the reasons why a vice president wouldn't make a difference is because presidential candidates attract more attention from both the media and the public, and during a busy campaign they're basically always doing something to get attention. Trump, the one-man media manipulator, has never had a hard time in this regard. Vance might pop up every now and then, when his comments in support of a national abortion ban surface or when he brags about telling his young son to “shut up about Pikachu,” but he's gone in a flash. Right?
But there is a growing belief that Vance may be an exception. As the race heats up, and as Harris leads in some polls, it is becoming clear that Donald Trump has lost a lot of steam over the past four years. Trump is very old, by his own standards is having trouble organizing his thoughts, and has much less energy than he did a few years ago. He can't campaign as vigorously as he did. That means he will have to rely on a running mate that everyone seems to hate.