A Lot of people have hard their papers go through in Canada eventhough they were on Deported in the United States. A friend of mine go his Canadian PR about 2 months ago even though he is on deportation in the US. He filed from his home Country and did not mention the US. Sometimes I tell people to trust their instinct and trust God thing will always workout well .
Did God instruct him to lie on his immigration application? He now risks that if anybody who knows about this ever gets mad at him and rats him out to CIC, he will lose his PR for lying on his application. He is not even safe if he gets citizenship because lying on your PR is about the only thing that can get you stripped of citizenship aside from renouncing it yourself.
Really, having been illegal in the US may not affect your Canada PR application. It may affect a study or work permit because they think you have a high risk of overstaying but when applying for PR, you will not be in the situation that you will overstay because you will have permanent residency. In my opinion, it's better to tell the truth on your application and have to fix whatever is barring you from entering than to get in on a lie and then have to be looking over your shoulder for the rest of your life.