Hi egyo,
We crossed the border last long weekend in BC, Aug. 3-5 with my two adult children whose PR cards were approved but not received yet. Mine was received just in time, Friday, Aug. 2. We already planned the trip so with or without the cards, we were ready to cross the border. Before that, my daughter called the CBSA first to confirm if we can go. The person from that office told her to just bring the expired cards and the print out of ecas status online that we got approval. Btw, we are from not visa-exempt countries also. When we were on the border going back to Canada, the Officer told my son (our driver) that his pr card is already expired. We told him that we renewed and approved, but haven't received the cards yet. Then he said, you can go.
Call cbsa to make sure everything is ok during in process, as well. I think, you should be ok.