The airline is required to do travel screening and this information is shared with CBSA. They have specific software installed for this purpose. If a reportable trace emerges, they won't allow to proceed with the boarding. Travel screening is used for all passengers requiring a visa. As for VWA passport holders, these checks are not implemented sytematically at the time being. So, if they actually decide to put your information into the system, they will learn about PR status (and request the card). Otherwise, they will just let the air passenger on board.
In 2016 VWA passport holders will have to pay $7 and receive an “electronic travel authorization” (eTA) before boarding a flight to Canada under a 2011 deal between Washington and Ottawa to better protect North America from security threats.