Why not, that's 0.02727 people per km², which is higher than Nunavut at 0.015 people per km², and close to the NWT at 0.036 people per km². Sure, it's not going to be an independant nation, but Nunavit certainly compares favourably against the other Inuit/Native populated territories, and if Quebec City decided to separate, Nunavit would quickly apply for the crown's protection.
Even Canada, at 9,984,670 km² has a relatively light density of 3.2 people per km².
And vast parts of Canada are completely uninhabited, just the same. Honestly, I don't understand your point, is that there aren't enough people in Nunavit to break away from Quebec to become their own Territory on-par with NWT or Nunavut?