That's a very good question. It depends on how you define sovereignty.
On the question of the Northwest Passage, it's more of a maritime issue.
On the question that is most pertinent, the extended continental shelf, that is the seabed. It's not an area that has been occupied or that ever could be occupied by humans. It goes beyond 350 miles into the Arctic Ocean. Human occupation is not a condition of extending your sovereignty for that seabed.
Certainly Inuit contributions and representation in the Canadian Arctic are important, but in the most near-term disputes on Arctic sovereignty, that human use and occupation will not be of importance. It's not even about the marine column. It's simply about the seabed and the ability of a country to be able to regulate that seabed of its extended continental shelf.