When I moved to Toronto last year, my husband is holding a working visa. Our whole family was still waiting for the approval of our PR application (which we knew would be very soon). We registered our kids to a public school based only on my husband's working visa and address proof (and maybe some other documents, I can't remember). A student visa is not required for the kids. You do not need to pay any school fee as long as you or your spouse holds a working visa.
For a Catholic School, I don't have any experience. Our friend's daughter are studying in a Catholic School in Toronto. He told us that it is not easy to get in a Catholic School.
補充: our case was we could get the PR card very soon. If u are not, I believe you need to apply for a student visa for your kid. Otherwise, your kid cannot stay in Canada for more than 6 months.