It is unlikely that they would cause scratches on a phone screen. However, it's not impossible if you have something hard (like sand or rocks) under the nails and use them to interact with the screen. In general, the thickness of a phone screen is around 1.1 mm, which is less than 7 (on the Mohs scale) of the hardness of the mineral, so it's more likely that the screen is scratched by harder materials, such as a diamond or sapphire.