I have the same problem as I have 3 months of work experience with a company for which I can't obtain employment proof. I don't have a necessity to claim those 3 months as they wont give me more points in EE.
I called CIC and the agent told me that one thing is them asking you in a form to provide your employment information of the last X years and another thing is the Express Entry profile where you claim work experience to receive points. So I's ok to not include all work experience in the EE profile if you don't intend to claim points from it. But you should mention it in your background declaration form when you fill your application.
I presume that people with ITA will get a personalized document checklist which will request employment proof for each of the positions you claimed in you EE profile.
I called CIC and the agent told me that one thing is them asking you in a form to provide your employment information of the last X years and another thing is the Express Entry profile where you claim work experience to receive points. So I's ok to not include all work experience in the EE profile if you don't intend to claim points from it. But you should mention it in your background declaration form when you fill your application.
I presume that people with ITA will get a personalized document checklist which will request employment proof for each of the positions you claimed in you EE profile.