If you have Single Sign On Installed on your website and you make the purchase of the Moodle Course based Product from the Woocommerce/Edwiser Bridge, you will be enrolled in the courses associated with that product. Your user account in Wordpress gets Linked to Moodle. After purchase, you will be redirected to the My courses page. Clicking on the enrolled Course, you will be redirected to Moodle where you can have access the course and you won't need a separate authentication for Moodle.

This functionality where the users are redirected to the Moodle site directly into the course without login authentication is available once you install Single Sign on extension.

If the user has purchased a Moodle course from WordPress then the user will be automatically linked to Moodle, therefore, the Single Sign On extension functionality will work then. But if the existing user has not made any purchase then you will have to manually link those users to Moodle by going into WordPress user's section and then select those users you would like to link to Moodle and then click on Link to Moodle account.