Anche no... L'interfaccia la puoi far implementare a qualsiasi oggetto....
Esempio con inner class...
codice:
public ... extends JFRAME{
   class Action1 implement SwingOperation{
     run()

     getDialog();
   }

   class Action2 implement SwingOperation{
   
     run();
     getDialog();
    }

   public void metodo()
   {
     SwingWorker<Void,Void> worker1 = new BackgroundOperation(new Action1());
     SwingWorker<Void,Void> worker2 = new BackgroundOperation(new Action2());
   } 
}