Yes, MassMailer does support the 'unsubscribe' feature. Whenever the recipient clicks on the 'Unsubscribe' link then 'Email Opt Out’ field is set to true for either Lead or Contact Object based on which one is used in the Campaign or Email Wizard. We also flag 'Invalid Contact' or 'Invalid Lead' field on Contact and Lead respectively.
Please note that any Lead or Contact set as 'Invalid' or if the 'Email Opt Out' filed is set to true, MassMailer automatically suppresses these Leads or Contacts from the list of recipients.