It is relevant, and there are cases like it. One is on this forum. Inlimbo's husband was working illegally in South Korea with a passport not in his real name. They were honest on the PR application, and they had a lot of trouble. The visa was rejected. They won the appeal, basically because they had a child, but the reprocessing took ages. I think she is finally at the end and will be getting the PR visa soon, but who knows, and they applied back in 2010.
The issue for CIC is this. Since the applicant has committed immigration fraud to enter one richer country, this is evidence that the applicant may be committing immigration fraud (a marriage of convenience) to enter another. The visa officers are already suspicious, so imagine how suspicious they become when they are handed proof the applicant has already committed immigration fraud.
I would message inlimbo and ask her what she thinks you should do.