A criminal record search with fingerprints is required before adopting a child in Canada. If this record search does not come back clear, then it is possible that your application for adoption will be denied. There may be exceptions if the record was completely unrelated to anything that would pose a threat to a child, especially if it was a long time ago.
We would recommend that the application for a Record Suspension from the Parole Board of Canada be started as early as possible, due to the length of time that it can take in some circumstances. The adoption process is already quite complicated, and it would be unfortunate to have to delay the process due to an existing criminal record.