Well usually they issue TRVs for 6 months, even though it all depends on the officer at the port of entry, he can allow a shorter period or god forbid deny entry, but that's rare, mostly it's 6 months. You must leave Canada by the expiry date of your TRV, or if you want to stay longer you need to apply for TRV extension, but only from Canada, I think at least a month before the expiry of your TRV. If it's granted you can stay longer, but again until the expiry date.
Staying in Canada as a tourist with a TRV does not jeopardize processing of your PR application. But, it is not possible to finalize your PR application if you do not leave Canada (if OUTLAND of course) because you obtain PR status only when you land Canada with COPR. In case they request an interview you need to leave Canada and go to Vienna. In case they need new medical/some additional documents like police certificate you would have to go home too.
But if they finalize everything without that and you get passport request during your stay in Canada I suppose you could send it by mail, I thought about it too, but I'm not sure it's a good idea not to have a passport in a foreign country. And they would mail the passport and COPR back to your home country and not your address in Canada so someone would have to mail it too you in Canada (supposing your TRV did not expire by then). With your passport you could flagpole to the nearest border I guess, I know little about it. Not sure where you are from but I need a TRV for US as well so this seems too complicated if you ask me. I will go home and then fly to Canada again with COPR. Hope this answers your question.
Other members, any thought about this? I have dilemmas on this matter too.
i don't have to explain that i suppose 
