I agree with BeShoo - yes, you can apply via the outland process even while you are staying in Canada. Be aware, though, that if an interview is required, you'll have to leave Canada to attend it at the overseas processing office and there is no guarantee you'll be re-admitted to Canada afterwards. However, being able to show that you have valid temporary status in the form of a visitor visa or visitor permit should help in that regard. Outland for applicants who want to stay in Canada during processing typically works better for applicants who are visa-exempt.
That said, an applicant never HAS to apply inland - they cannot force you to apply inland because inland sponsors forfeit the right to appeal a refusal. And the inland process requires that you remain in Canada, even if you don't have valid temporary status - which puts you at a disadvantage. The outland process does not have a residency requirement - you always have the right to apply through the embassy that represents your home country, even if you aren't living there. You do, however, have to have valid temporary status in Canada if you intend to remain in Canada while awaiting finalization of your PR ap. And that's also the best way to "prove" your co-habitation for common-law qualification if the "living together" has been accomplished within Canada. It can put you at a disadvantage to try to prove cohabitation in a country where you didn't have the right to stay.
Be sure you apply separately from the PR ap for your visitor extension - but include proof of your relationship, financial support from your partner and the PR ap in process with the extension application. Also, track the mailing and get delivery confirmation (this applying online is new and I'm not sure what type of confirmation you get, so be cautious) - you'll want to be able to demonstrate that you have "implied status" to remain legally in Canada if the approval of the extension doesn't come before your current status expires. It's currently taking about 55 days to process those.
