No, there is also the option of including your customers in the tracking process without registering a new user account in YouTrack for them.
When a customer sends an email to your support email address, YouTrack automatically generates a new issue and saves the reporter's email address (without registering a new user account).
If you then add a comment to this issue or change its status, the reporter will receive a notification about it.
Every response to the issue from the reporter is in turn saved as a new comment in the issue. Your support team can thus process all customer inquiries in YouTrack (as fully functional users), while your customers receive the desired information via email.
More information about Help Desk Support in YouTrack and a step-by-step guide for configuration can be found here.