The insurance industry has access to an index for claims based on a social security number. It can show some things like personal injury and work comp claims. Also, in California, the public has access to EAMS, which shows some public records information on workers comp cases filed with the workers comp courts (WCAB). You can check it here: https://eams.dwc.ca.gov/WebEnhancement/
you don't mention what type of background check. If you mean for employment, yes, they could find it but it's unlikely they would go that far. If you mean an FBI background check...count on it. Workers' comp. cases are public records it just depends on how much trouble someone wants to go to to check.