I'm not sure because I don't have the need, so never looked into it.
I do know that you can apply and get a Canadian passport on urgent basis (2 business days) but you would need to prove your reason of urgency. I'd suggest to take this option. Also let them know about your case, maybe they can expedite your certificate too.
Otherwise I don't think leaving Canada would ever be a problem on your existing passport. It is re-entering which would require Canadian passport, which you can get in another country too if you have your citizenship certificate mailed and apply for Canadian passport at the nearest Canadian embassy/consulate. Again I'd not suggest this option, coz not only it has more potential for complications, we also still have pandemic issues which makes all such things quite hard to predict.