I’d hesitate to say it’s impossible, but I think it’s highly improbable. Flights from India to Canada are commonplace, so I’m sure they have the routine of checking visa, passport and PR card validity down pat.
As Buletruck implies nobody here is going to say is impossible but the checkin agent will have a procedure to follow to ensure that before accepting someone for checkin that they have a valid passport and a valid visa for Canada unless visa exempt.
If from a visa exempt country they would have board/no board check for an ETA, if a valid passport but non visa exempt with no visa (or any other permit) then logically the traveller would be expected to present a valid PR card or PRTD to pass the board/no board check.
As said by all means anyone can try their luck but be prepared to have a plan B to rebook should you not succeed. Good luck
Looking at your timeline, I am curious if you even meet the Residency Obligations requirements. If you don't, you may have many more problems when/if you reach the border or apply for a PRTD.