No, I don't think you would be examining the Constitution.
The Supreme Court of Canada provides a two-part test to determine whether a proceeding is administrative, penal or criminal in nature.
The 2015 Guindon decision from the Supreme Court of Canada, which basically reiterates the test from Wigglesworth and Martineau, gives us the guidelines to assess a situation and to determine whether we are dealing with something that's purely administrative in nature and procedure, and therefore the administrative law applies, or whether it's criminal or penal, and therefore the higher standards apply. This, for me, is the exercise that must be undertaken when examining Bill C-77.