If you add Settings to a Class Library project in Visual Studio (Project Properties, Settings), it will add an app.config file to your project with the relevant userSettings/applicatioNSettings sections, and the default values for these settings from your Settings.settings file.
However this configuration file will not be used at runtime - instead the class library uses the configuration file of its hosting application.
I believe the main reason for generating this file is so that you can copy/paste the settings into the host application's configuration file.