If you're referring to the board discussed rivalry between NMU and MTU, no. (Marquette and Houghton, respectively.)
If you're referring to the high school hockey rivalry that hardly gets any mention outside of the UP, you'd be correct. The Calumet Copper Kings and Houghton Gremlins have quite the sports history. Being practically the two biggest school districts in the region for a century helps. (But they're still tiny compared to any other school district anywhere else.)
If you ever are bored enough and want to fall down a Wiki rabbit hole for an afternoon, Calumet was once the hot bed of copper mining in the UP. Lots of labor strife was sparked in Calumet with the copper strike of 1913 where miners demanded 8 hour work days, improved wages, and elimination of the "widow maker" one man drills. It came to a head at Christmas of 1913 when 70 miners and their families were crushed to death in a panic when "Fire!" was falsely yelled in a crowded theater. The closure of the mines once the easy to extract minerals were taken contributed to the town, and regions, downfall. It's the tale of pure capitalism and the stubborn idiots who remain.
It's also gorgeous to visit if you enjoy nature.