So what it depends on is the click. Where your click takes you, whether it uses a URL parameter or goes to a unique page. If the user has javascript or cookies blocked it could potentially prevent the registering of the unsubscribe.
If you really wanted to do it, I'd create an unsubscribed segment or form 2.0 with conditional logic, and create a smart campaign >> clicks link in email contains OR visits webpage contains then change data value, unsubscribed = true. But on the specific landing page you create, if you were to use a segment (unsubscribed = true), then you could filter the form dynamically to show text instead - "thank you for unsubscribing".
I just wouldn't want to do something where a user could potentially slip through the cracks & not be unsubscribed, a link could get tracked to the wrong person & someone could unsubscribe someone else. The form just makes it certain.