I think your situation would be fine because in order to keep your status as a permanent resident, you must live in Canada for at least two years within a five-year period i.e minimum of 730 days physical presence in Canada at the 5-year mark. So at least in the 4th year after your initial landing date, you might have to live in Quebec in order to maintain your residency obligation.
PR residency obligation is a federal regulation, one can live anywhere in Canada to satisfy the obligatory 730 days. Once a person becomes PR he/she would be protected by the Charter of Rights and Freedom, and the mobility clause allows the person to move and to live in any province/territory in Canada. That being said, the Quebec Investor will still require an initial Quebec address to get their PR card.