I'm not sure if possible, because the Roundcube installation 'requires' DB (see this install how.to
but then again the DB configuration in db.inc.php file is:
Edit the db.inc.php file and replace the below lines with your database access details
$rcmail_config['db_dsnw'] = 'mysql://roundcubeuser:roundcubepwd@localhost/roundcubedb';
so in this line the "database" is defined, which probably could be also a flat file (text), but it's not known what should it contain.