i heard one of my colleage saying her friend pay to attend a short course to apply for a student visa so that she could stay and wait for the applicaiton
if you are the visitor, wonder why they did not put an stamp on your passport.
if that's really the case.. then try your luck lor. since you are leaving. they should not be asking any question about that. but not sure if they actually have the record of your overstaying. and might blacklist you on your next travel to canada
Don't take the risk..
Especially, if you are applying for the sponsorship application.
They have system record to show that you stay overtime then they might not continue with your application once they found out