No. User account to the Rancher support portal (hosted on Zendesk) is not a necessary precondition to being able to file a support ticket. With an active subscription to a Rancher support plan, support tickets can be filed by simply sending an email to firstname.lastname@example.org and continuing the correspondence via email.
User account to the support portal is for the purpose of being able to access all your tickets in one place in a secure way and interact with them. As well as, being able to access any knowledge base articles that are available to Rancher customers only.