It would be nice to have an option for JIRA Administrators or Service Desk Agents to create Service Desk Customers without the need to send an invitation e-mail.

Workaround

For now, the only way to do so without the invite is through the default user creation in JIRA.

1. Go to Administration > User Management;
2. Hit Create Users in the top right of the page;
3. Fill the form with user's details;
   Uncheck "Send Notification Email".
4. Create the user;
5. On the right of the newly-created user, click Groups;
6. Add groups you want to have the user included;
   If you do not want the customer to access JIRA itself, remove it from the jira-users group (valid for JIRA instances with "default" schemes)
7. Open up the Project Administration page for the Service Desk Project you want the user to be added;
8. Go to Roles (on the sidebar);
9. Add the user to Service Desk Customers role;
   Note that this will only work if you use the new Service Desk licensing model (unlimited customers).