I would say that through a voluntary census, information gathered becomes unreliable and unusable for the very specific reasons that have been mentioned here already. Any other surveys on social services are also compromised without a reliable, comparative demographic scale to be used alongside.
To answer your question, I think it's the comparative demographic scale that would result from a long-form census that could then be applied to any other voluntary census. You do need a base that you can use that's reliable.