Is mode C required for CVFR in Canadian Class B airspace?
The vast majority of GA airplanes have Mode C transponders and when you ask for the clearance, you will be given a transponder code to squawk.  If you don't have one, you have a problem and you probably won't get a clearance except in special circumstances.  Not only do you need a  Mode C transponder, it has to be calibrated and certified every 2 years by an AMO.

You could call Terminal while still clear of the Class B, tell the controller you are no-transponder would like to go from A to B, and see what happens: the controller may let you transit by reporting position at specific points if the path is out of the way.  Or maybe not.

Better yet, call the applicable ATC unit on the phone and find out if you can get permission to transit Class B non-transponder for a particular reason.

As a general practice however, the answer will almost certainly be no.  Just go around or under.