Yes, the default configuration uses H2 In memory database, if you change that configuration to use a different database like for example mySQL you will be able recover the state of the process. Look in the documentation to see how to change the configuration. If you look inside the application you will find a persistence.xml file where the persistence data source is defined.
Comment out 'hbm2ddl.auto' property in hibernate.cfg.xml file if you do not want the tables auto created after you restart.
You can locate this file in gwt-console-server\WEB-INF\classes.
<!-- Drop and re-create the database schema on startup? -->