Not legally. If you have a lease in your name in Montreal, and no stronger evidence of primary residence elsewhere to make the claim that the Montreal place is for vacation only, you will need to switch your residence. Also, if you intended to use Quebec health services you will need to get your health card for that province.
I believe the only people who can legally do what you are describing are university students from out of province.
It isn’t a matter of where you physically are on December 31st.