Memberships of disabled membership types do not appear on the membership tab BUT do throw duplicate Membership Warning
If a contact has a Membership of the Membership Type "Student" and the membership type "Student" gets disabled On the contacts membership tab you will see no memberships but when you try and create a new membership for this contact a "Duplicate Membership" warning will appear.
To some extent this makes sense because if one were to re enable the disabled student membership type and a user had created a new membership that could be problematic. However from a UI perspective it seems like it would be useful for disabled memberships to be listed.