Nobody can have 2 status as the same time such as Study permit and Work permit. When you have your study permit, then you apply WP with a form, that form's name quite clearly. It means you're going to exchange your status. After you got your new permit, you are no longer in conditions/status before.So I just got off the phone with IRCC and apparently one does not invalidate the other.
When you got your wP there is conditions as well, on paper quote.