My only comment would be that it would be illegal under the DNA Identification Act for the officials in the DNA data bank to send or communicate information from the data bank except as permitted by the DNA Identification Act, and those cases are very restricted, so that the only thing they could unilaterally send abroad as a profile for comparison would be from a crime scene. So unless the refugee left their DNA at the crime scene of a designated offence in Canada, that would be the only profile that could be sent abroad. And it would normally be anonymous, because they would not know who it was.
So it's really unlikely that your scenario could take place.