Can I add extension methods to an existing static class?

No. Extension methods require an instance variable (value) for an object. You can however, write a static wrapper around the ConfigurationManager interface. If you implement the wrapper, you don’t need an extension method since you can just add the method directly.

 public static class ConfigurationManagerWrapper
 {
      public static ConfigurationSection GetSection( string name )
      {
         return ConfigurationManager.GetSection( name );
      }

      .....

      public static ConfigurationSection GetWidgetSection()
      {
          return GetSection( "widgets" );
      }
 }