Hi,
here is my very recent experience, maybe you will find it helpful. I became a temporary worker in Quebec in 2015. Decided I want to apply for PR not too long ago (end of year 2016.) I did not apply for CSQ, decided to go through express entry and move out of Quebec if required. I got selected and applied under the CEC class for PR in April 2017. The application went smoothly and I did my landing in Toronto few weeks ago. During all this time I was and I am still employed in Quebec. The officer in Toronto did not seem to care about my address being in Quebec.
So in short, you can get the federal PR even while still being in Quebec.
There is a downside, that I don't have the CSQ. So far I run into issue with RAMQ, that I am not eligible to get public health insurance in Quebec. You can pay for private health insurance though. Living and working here seems to be OK. There are probably other benefits I can not get, but as a short term solution I am fine with that.
If anyone has this experience - I don't know and would like to know, if there is any option to obtain CSQ after you became PR through other than Quebec classes?