Don't think so McC. The Telfer School of Management will remain permanently in the Desmarais Building.
Here is what the university web site says about who will use the new tower..
The new tower will house the Faculty of Social Sciences and will include research space in priority areas such as neuroscience and experimental psychology, economics, public policy and management.
The facility will feature a number of new multimedia classrooms and significant new student spaces throughout. A 225-seat classroom and a large multi-purpose hall are proposed for the upper levels. The new Faculty of Social Sciences Building was designed to be expanded incrementally in the future and to eventually replace Vanier Hall with a larger facility
The combined buildings (Vanier Hall and the new tower) will be able to house the following:
7,000 undergraduate students
1,000 graduate students
250 researchers and professors
So , it appears the Social Science Faculty will be the primary tenant of this tower. Social Science does currently have some elements housed in the Desmarais Building.It is they who will likely be moving over to the tower.The Faculty of Soc Sc, and the the Telfer School are two separate entities within the university.
What I have missed in the past is the statement that the new building may someday be expanded and replace the old Vanier Hall (about 60 yo I think) it is attached to.