Yes, but instructors should ensure that initial drafts are not submitted to the Originality Report database, or else false positives will be found for the later drafts.
Instructors should create an assignment for each draft. In the Optional Settings, instructors should set the "Submit papers to:" field to no repository. For the final paper, instructors should create a new assignment and let the check run as the instructor normally would. See detailed instructions at Turnitin.com.
For other common questions, please read the Turnitin FAQ.