In live in BC, when I first came to Vancouver with my then, 15 year old son, without either PR or a work visa, there was no way they would let my son attend school. Applying for a study permit for him was also a no go, as they required me to pay for the schooling and at 5000 dollars a term, that was way beyond my budget.
I got lucky, I got a job, LMO and work visa within 6 weeks of arriving, thus as soon as I had that work visa, he could start school.
When I applied for PR, my work visa was also due to expire and the time lines overlapped. I was on implied status and during that time the school board allowed my son to still attend school. They did however, inform me, that once I received AIP and an open work permit, that I still needed to prove I was working to allow my son to attend school.
On the other hand, reading the CIC website, if a child is due to start kindergarten, then neither study permits or work permits are needed.
I have no idea what other Provinces are like but Vancouver is really strict about letting kids into the public schooling arena.