Do I have to have a membership plugin to secure my course?

No. Since students have to be registered and enrolled into a course to see the course content, anyone surfing your site will not have access to the course content. The only way a person can have access to your course is to be enrolled for that course. The only potential course type content that anyone can view is a course outline, but not the course progress page. The membership plugin can add an extra layer of security, and helps to automate the enrollment processes and manage users to make your life easier. However it is not required to secure WP Courseware.