Yes, but an emergency passport comes out MUCH faster than a PRTD! My husband's family has had all of their documents stolen on a one week trip to Mexico (theft happened on the second day), and they made it home in their original scheduled flights, after having gotten emergency passports from the Embassy.
Correct. When you visit a Canadian embassy as a PR ... they simply don't want to know. Happened to friends.
Equally when a different friends Canadian passport when missing - much easier process.