Yes thats possible, you need to work with the classes as i wrote in the documentation.

{
    module: 'clock',
    position: 'top_left',
    //Set your classes here seperated by a space.
    //Shown for all users
    classes: 'default everyone'
},
{
    module: 'example_module2',
    position: 'top_left',
    //Only shown for name1
    classes: 'thierry james'
},
{
    module: 'example_module',
    position: 'top_right',
    //Only shown for name1
    classes: 'james'
}