When you are in Canada, checking in for a flight leaving Canada, AC or any other airline really doesn't give a damn about whether you are in Canada legally or not, how you have entered the country etc.

They will not want to see documentation of your status in Canada. They need to see valid, admissible ID for the destination they are sending you to.

As a dual citizen, I always leave Canada on my overseas passport if I travel to my other home country. That overseas passport does not have the required ETA, visa etc. to justify my presence in Canada. No airline ever had a problem with it.