Have scientists actually studied the effect of Viagra on premature ejaculation?

As far as large scale clinical trials, no. There have been some smaller studies that attempt to treat premature ejaculation with Viagra along with other substances, and while these studies are encouraging, they’re still preliminary. Neither Viagra nor any of its competitors has been approved by the US Food and Drug Administration for treatment of premature ejaculation, although doctors can prescribe the drugs “off-label” for that purpose.