Technically. Same with basketball, technically. The NCAA only officially has a single Division I, in both sports.For football but not hockey.
But we all know there are defacto levels within the division, in both sports. Tommies in men's hockey are being looked at for the new CCHA, which will be equivalent to the previous WCHA, which is a level below the NCHC and Big Ten.
Bball the Summit League is competitive, but definitely a low major conference. And they'll probably need time to become competitive with the Dakota schools.