Yes. Standard Moodle course/activity backup (the MBZ file) contains all the information needed to restore the whole workshop in another Moodle (or in the same Moodle but in another course etc). However, to be able to include user data (such as submissions and assessments in case of Workshop), the user performing the backup must be granted with a privilege - see http://docs.moodle.org/en/Backup_of_user_data. If your administrators did not give you such permission, you won't be able to include user data in the backup. You will have to ask them for either giving you required permission or making the backup for you by themselves.
Workshop
backing up from Workshop
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