There have been eight seasons where Duke was #1 in the AP pre-season poll:
http://www.sports-reference.com/cbb/schools/duke/
In the seven completed other seasons, Duke won at least one sort of championship (ACC regular season, ACC Tourney, NCAA regional, national).
http://www.sports-reference.com/cbb/conferences/acc/
Will be interesting to see what hardware this 2017 squad might bring home.
2017
2011 – ACC Tourney champs
2006 – ACC Tourney champs, ACC regular season champs
2002 – ACC Tourney champs
1999 – Final Four, ACC Tourney champs, ACC regular season champs
1992 – National champs, Final Four, ACC Tourney champs, ACC regular season champs
1989 - Final Four
1979 – ACC regular season champs