I'm waiting for UBC as well. The deadline for my program was Dec 1 and I submitted my app in mid-October so I'm anxious to hear their decision. I was told February to March was the timeline but I still check multiple times a day
I would definitely email the graduate department. You have a shot. I know at UBC the grad admissions coordinator of my program gives an extra two weeks or so after the deadline for additional documents to come in. I had a similar issue, except my reference submitted his literally the day before the deadline.