Being illegal in US will not affect ones case if one wants to migrate to Canada, not unless if you have a CRIMINAL RECORD.
I am in the same situation, I processed my papers while in US as FSW1 and I am now a permanent resident of Canada, started processing last January 2009, got our visas December 5 2009 and landed in Toronto last March 2, 2010. So I can vouch that if you are illegal in US you can still apply to Canada to become a resident. I dont know how it goes in Quebec, but as long as you meet the minimum requirements you will be fine.