Entirely. Quebec would probably be partitioned if they got independence due to a number of factors, like the reservations, the number of anglophones, and the north of the province.
Technically-speaking a good chunk of North America (Ontario, Michigan, Ohio, etc, etc.) was carved out of what was Quebec.
As far as present-day Quebec being broken up into smaller provinces, I could see maybe the Gaspé and the Gulf of St. Lawrence islands wanting to form their own province, but they don't have enough people. Ditto Nunavik.