No. There are a lot of students who aren't funded. You probably already know that federal and provincial granting agencies don't provide funding to all students. Often it's the professors who have to pay the people who do research with them.
There is also a direct link between funding and graduation. The Canada Research Chair on the Transformations of Scholarly Communication at the University of Montreal told us that a student who receives funding is more likely to graduate than a student who doesn't.