The COVID related advisory doesn't mention full-time vs part time, but it does require essential employment: Essential (non-discretionary) travel for a temporary worker
Your travel is essential (non-discretionary) if you’re in either of these situations:
You’re a worker who
has a letter of introduction for a work permit (open or employer-specific), and
has a valid job offer, and
can work once you’ve completed your 14-day quarantine in Canada (unless you’re exempt)
I dont even see essential specified for those who just need to activate POE upon entry.
As of May 8, 2020, if you’re taking part in the Working Holiday, Young Professional or International Co-op categories you can come to Canada if you have:
a valid job offer which includes a written note from your employer in Canada that says
their business is continuing to operate (whether essential or not)
Essential refers to travel for reasons that are non-discretionary and non-optional. The emergency orders under the Quarantine Act do not allow people to travel to Canada for optional or discretionary reasons, such as for tourism, recreation or entertainment.
Essential (non-discretionary) travel for a temporary worker
Your travel is essential (non-discretionary) if you’re in either of these situations:
You have a valid work permit and normally live in Canada. This applies even if you’ve been laid off.
You’re a worker who
has a letter of introduction for a work permit (open or employer-specific), and
has a valid job offer, and
can work once you’ve completed your 14-day quarantine in Canada (unless you’re exempt)
Non-essential (discretionary) travel for a temporary worker
Your travel is non-essential (discretionary) if you’re in either of these situations:
You have a letter of introduction for an employer-specific work permit, but your employer has closed their business due to the COVID-19 outbreak.
You have a letter of introduction for an open work permit, but you don’t have a job contract and are planning to find a job once you arrive in Canada.