Gradebook has the history and you can choose to import the old information or not. The Quiz module doesn't do anything with that option, though, so if they are allowed a limited number of attempts at a quiz that will be a problem.
For example, if it's set where they get one attempt at the quiz, that means one shot FOR LIFE, even if tey enrol in the class again three years later. If that matters to you, if you'd like Quiz to respect the choice to not import old information, you can express your needs here:
http://moodle.org/mod/forum/user.php?id=1468589&mode=discussions
We have a fixed verson are the discussion is whether or not the fix should be accepted into Moodle.