Yes, they have to show that they tried to hire a Canadian.
This is what is specified on the BC PNP website:
"Meet domestic labour market recruitment requirements.
Subject to verification, the PNP will consider this requirement to be met if:
Your employee has obtained a valid work permit from Citizenship and Immigration Canada and is currently working for you,
OR
You have provided evidence of a genuine effort to recruit from the domestic labour market and are able to demonstrate the results of your recruitment efforts, including advertisements based on the following minimum requirements:
For Skill Level 0 or A jobs (based on the National Occupational Classification)
Recruitment advertisement must be for at least 14 days.
Acceptable recruitment advertisement locations include:
Recognized job posting websites
Professional association websites
National newspapers, professional journals or newsletters
The 14-day recruitment advertisement requirement may be waived for the recruitment of senior executives or highly specialized senior managers and professionals. In these cases you must demonstrate targeted recruitment actions consistent with industry norms, such as the creation of an executive recruitment team or the hiring of a specialized human resources recruitment agency.
For Skill Level B jobs (based on the National Occupational Classification)
Recruitment advertisement must be at least 14 days.
Acceptable recruitment advertisement locations include:
Recognized job posting websites
Professional association websites
National newspapers, professional journals or newsletters
Advertisements must include:
Company operating name
Job title and duties
Rate of pay
Location of work (local area, city or town)
Contact information
Skills requirements for the job including:
Education and, or, qualifications
Work experience"
Hope this helps!