I think we have enough experience in Canada with existing surveys and from other countries to know there would be a sharp distinction in the response rate. I'm personally not troubled if the response rate dropped, from almost 100%, even 20 or perhaps even 40 percentage points, if it was still representative of the population. I think the more troubling thing is that, if the experience in Canada and elsewhere is that it's not going to be representative, you would get an over-weighting of--let's face it--white, middle-class Canadians and a dramatic under-weighting of some other groups, particularly the poor and the very wealthy, particularly some recent immigrants, and certainly first nations.
Over time you could probably sort that out, but it would probably take three or four cycles of a survey to understand what the weights are. In the meantime, I think the data could actually be worse than not having anything. It could be misleading. You may be making misleading inferences because you don't actually know how to properly weight the groups that might be underrepresented.