I happen to know a lot of my friends, who were CP applied and got the greencard.By law, US has the burden to prove if you are really a CP. Most of the time, US has no resource to do so, unless your activities harm US national security. Also by law, if you lied on your application, your greencard or even citizenship resulted from gc could be reversed. Well, there is really very few people will get caught if you keep your nose clean in US.