Raven,
I had mentioned NO after reading from http://www.cic.gc.ca/english/information/applications/guides/EG7TOC.asp, the OFFICIAL WEBSITE which you can't dispute.
Extract pasted here :
"Do you intend to reside in Quebec?
If you intend to reside in the province of Quebec, you do not qualify under the Federal Skilled Worker Program.
Under the Canada-Quebec Accord on Immigration, Quebec establishes its own immigration requirements and selects foreign nationals who will adapt well to living in Quebec. If you intend to come to Canada as a Quebec-selected skilled worker, you must first apply to the Ministère de l'Immigration, de la Diversité et de l'Inclusion (MIDI) (in French only). "
Hence had mentioned that though technically allowed, it may lead to problems. I agree with Future_canadian that after PR card is issued after 3-4 months, no one can stop you from working in Quebec, but why take a chance ? If you want to work in Quebec, why not apply through their dedicated programme ?
Hope we are on the same page.