If I worked or studied in Canada illegally, can I use that experience in my Canadian Experience Class application?

No. Any experience you list in your application under the Canadian Experience Class must be legal to be valid. You cannot have worked or studied without authorization. If you have ever done so, your application will be refused.

Note: Completing an Express Entry profile is the first step to immigrate to Canada permanently as a skilled worker. Completing an Express Entry profile does not guarantee that you will receive an Invitation to Apply for permanent residence. An Invitation to Apply for permanent residence will be based on your score and rank in the Express Entry pool using the Comprehensive Ranking System.