Whether you are a main applicant of a dependent, everyone will have to declare that they have intentions to reside in Quebec. Once you get your CoPR and PR Card, there is no condition attached to it (i.e. not a requirement mentioned in your PR documents).
If we look at the second fact, you CAN have more than one homes in Canada. So, as long as you retain and maintain proof of residency is Quebec, you will not face any problem in terms of signing up for "Reside in Quebec". But there are some ramifications, such as absence of 183 days health insurance rule. Do study them. Having said that, Canadian Permanent Residents have full mobility rights. This means that, unless you are otherwise legally restricted (bail, bond, etc.), you can move to any city or province in Canada and live wherever you wish. However, as a new immigrant you may not have access to some of the Quebec-funded services for immigrants that come to that province via their provincial selection process.
Obviously they can't follow you around and make sure that you stay in the province that nominated you but what it means is that you might run into troubles later on. Maybe citizenship and such or if I start going in and out of a province that I don't "reside" in, the border agency people might question me and my intent. It's all about intent, if you can show that you have a place in that province, a job in the nominated province, your kids go to school there etc. it doesn't matter where you enter. (but that's just my opinion)