I rather suspect there still would be. Perhaps less. But a lot of the conspiracy theorists actually believe that governments (or their authority of choice) have manufactured the disease. There are also reports of people not believing the disease is real while they're dying in hospital.
Yeah. I've made this point to friends too. In some sense covid sits at exactly the pessimal spot. Any less severe, and we'd have just let it roll over us without the societal breakdown. Any more severe and the mitigation strategy couldn't have become a political issue.
Maybe there's a side-channel attack where we can convince the conspiracy folks that this actually is a Chinese bioweapon designed to destroy the political cohesion of the west, so they should get on board and get their shots. Think it'd work?
Ironically, many of them already believe that. Conspiracy-theory beliefs (i.e., evidence-free conclusions) are a symptom of underlying mental illness, which inhibits critical thinking skills. As such, they have no problem holding completely contradictory viewpoints.