I'm not familiar with the design of the replacement for the Canadian long-form Census so I'm not going to address that in particular. I do want to address your assertion that a voluntary survey is the same as a self selected survey. In a self-selected survey any member of your universe may choose to become a respondent and you typically will not have any non-response followup (the people that come and bug you if you don't answer the survey.) Now a voluntary survey simply means that you are not required, by law, to answer. So you can have self selected voluntary surveys, non-self selected voluntary surveys, and non-self selected involuntary surveys. I don't believe that the concept of a self-selected involuntary survey really makes any sense, so a it's probably safe to say that a self selected survey must be voluntary but the converse does not hold.
In both voluntary and involuntary surveys you will experience non-response. This is a problem since you now have a portion of your universe which you are unable to measure. There are various ways to adjust estimates to try and reduce the non-response bias, but the best is to go back out and try to convince people to respond. I don't know about Canada, but the only difference the legal requirement has in this process in the US is that if response is required by law, we add a line along the lines of 'Your response is mandated by law.' There are fines and jail time that go along with them, but to the best of my knowledge they're never used. In fact, at least for business surveys, the fine never even is mentioned since many businesses would rather simply pay the fine than spend the time to respond. Really, the only way you'll have an additional problem with a voluntary survey is if the people who only respond because we say they must are different from the people that will not respond regardless.
I'm a little surprised that they made it voluntary, but that alone isn't sufficient to destroy the quality of the survey. If nothing else, I'm curious to find out what exactly they did. Fortunately I've got this wonderful Internet thing to help.