Hi Chad,
Qualifying a Lead will remove it from the Nurture. The Lead should stay on the Marketing List per CRM behavior, but the default View, "Associated View", will filter to only show Active records. Your Inactive Lead would still be on the list, however, and can receive ClickDimensions emails. If this isn't desirable, you can add a quick statement to your Marketing List to only include Active records.
Thanks for using the forum and please let us know if you have questions!