No they don't
even before this message, I can tell when customers have non-Apple displays simply by looking at them. They’re usually tinted blue & desaturated. I saw this thousands of times while I was a genius and even when customers bought the phone secondhand and didn’t do the repairs themselves.
this message helps customers make sure their secondhand purchase or 3rd party repair was done well even if they’re not accustomed to seeing numerous iPhones a day to tell the difference solely based off looking.