Yes. In fact, a couple of programs were put forward, one in 1973 and another in 1983, and take-up was much less than had been anticipated. There may have been a fear of coming forward or of receiving some sanction for having been in Canada without status.
Certainly given the debate in the United States, while the scope of the problem is much larger there, it is a difficult issue. There would be security concerns, and certainly countries such as Spain and Italy, which have undergone a number of regular “amnesties” over the last couple of years, have incurred the disfavour of some of their EU partners, given labour mobility access across the European Union.