@Meylis Correct, you can leave before you receive the cards. And yes, if you do not have the card on re-entry, you’ll have problems. In fact, you won’t even board the flight to leave your country of origin as it’s required since you’ll have no visa.
You have to figure out a way of having the cards sent to you to ensure your re-entry into Canada. If the address you provide is a friend’s or a relative, they should be able to send them to you. If it’s a UPS store, they should be able to forward all your mail to which ever address you give them.
All the best.