This is correct. The easiest way to test it is to create a user with a throw-away email address and try suspending and unsuspending them through the UI.
When a user is suspended, a suspended_until and reason must be set. These fields are displayed to a suspended user when they attempt to login to the site. You can customize this text by searching for login.suspended_with_reason on your Admin / Customize / Text page.
Unless you enable the hide suspension reasons site setting, there will be a notice that the user has been suspended displayed on the usercard and profile page of the suspended user. If you enable the hide suspension reasons site setting, the notice will only be seen by staff.