Hopefully for some it will, and obviously every little bit helps. However, he was met with some boos from supporters at one of his rallies over the summer when he mentioned having gotten the vaccine, so I imagine there’s no convincing some of them.
We'll learn some things about which direction the causal arrow runs from how this plays out.
I wouldn't know since I don't frequent such websites, but is it possible that Trump and Fox were only reflecting the views of the lunatic fringe of the conservative movement back at them? If so, I'm not sure if that level of cynicism makes it better or worse.
As I stop and think about it, the click-based nature of our media means that the heaviest consumers of that media have much more of a voice in the content that gets put out there. This is disturbing because the most enduring finding in the political behavior literature is that the most engaged citizens are
weird relative to the rest of us.
Perhaps polarization is better thought of as a self-perpetuating feedback loop than as a product of the interaction of gerrymandering and changes in the mass media.