No. South Dakota State University began a transition to Division 1 in 2004. In football, SDSU is a Division 1-AA school that plays in the Missouri Valley Football Conference and in basketball, they play Division 1 in the Summit League.
It is really cold up there. Weather may play a part in North Dakota's low population but other factors include the fact that North Dakota is an agricultural state, so much of the state is farm land. The history of how the state was settled played a part along with the fact that, for the pioneers and settlers, North Dakota was a long distance away from their homes and families in the eastern United States.
NFL player Matt Veldman played for North Dakota State.
NFL player Marcus Williams played for North Dakota State.
NFL player Joe Mays played for North Dakota State.
NFL player Brock Jensen played for North Dakota State.
NFL player Billy Turner played for North Dakota State.
NFL player Ramon Humber played for North Dakota State.
NFL player Craig Dahl played for North Dakota State.
NFL player Paul Cornick played for North Dakota State.
NFL player Bryan Shepherd played for North Dakota State.
Well, all sports are played in North Dakota; however, there are no teams associated with professional sports leagues (NFL, NHL, etc...). There are teams which play baseball in the American Association and the University of North Dakota has NCAA Division-I sports in Football, Hockey, BAsketball, Baseball, Soccer, and others under the school name of "The Fighting Sioux" of which there is much debate.