Nope, as previously said, PRs have the right to enter Canada so they can't be denied entry by CBSA at all... CBSA can simply look it up in their records.
It's just that commercial carriers (air, land, water) will deny them boarding, if they are non-visa exempt. That's why a private car is the officially sanctioned workaround if using a COPR. There are, of course, a few cases of people on this forum managing to find loopholes by boarding with a visa-exempt passport or valid TRVs acquired prior to getting COPR.