I have also always wondered if using the barcode on the back of the SM or CRC card would work. I inadvertently got to find out the other day because I left my BP in my shirt pocket that I changed out of and did not have it ready when I boarded.

I told the GA I didn't have my BP and he proceeded to look me up on the computer to print out a BP when I asked him to try the barcode on the back of my CRC card. To our surprise, it beeped and spit out a paper receipt with my seat on it!