Can you know how much damage an STD has caused?

Probably not. It depends on what venereal disease it is and how long you had it. Syphilis is really nasty because it eats holes in the brain; it's suspected that both Adolph Hitler and Al Capone had brain damage due to untreated or undiagnosed syphillis (which wasn't really treatable back in the 1920s and 1930s.)

Since the damage is to the brain, it may not be discoverable except through an autopsy or through an MRI or CT scan of the brain. Minor damage might not be detectable.

Some STDs - I believe gonorrhea is one - can render a person sterile, and there would be no way to tell unless they tried to have children and had trouble, then had testing done.