I suspect tens of thousands of people don't even know if they have a criminal conviction for the possession of cannabis, who don't understand the implications of it. Colour me extremely skeptical that the Government of Canada can't do a search through their own conviction database.
I deal with police officers every day in my professional employment; they all have access to CPIC, that is their centralized database. They put someone's name in, they get the records of conviction. Surely as it's a database, you can do the opposite, put in the records of conviction to get the names.