Overstaying the VISA in US will have no impact on your Canada PR application, but you have to fully disclose the history entirely (when and how you entered US, and why you decided overstay, with all VISA attached, if applicable). Also, as somebody else posted FBI Rap Sheet will not contain any of your immigration record (If you had warrant of any kind, including immigration, then it will show on the FBI Rap Sheet), and by applying FBI Rap Sheet, it will not lead you to be exposed to ICE. And most likely your case will be transferred to your local VO for process, and if there is an interview request, you have to leave US to attend the interview, which means you will be barred 3 or 10 years or even life time from US, depends on how long you lived US illegally or if you ever misrepresented to the US immigration Authority.
As long as you are 100% honest to disclose the US immigration history, and you are qualified to immigrate to Canada, CIC will approve your case and issue your COPR without asking any additional documents.