Yes IMO they should. Something stating the international flying and it's passport requirements (please verify your expiration date) and minimum bag check all should be reiterated yet again.

Some airlines do offer online check in if passport info is already entered or they offer the ability to enter it.

Though that just mandates another check at the gate to verify the passport info rather than a quick BP scan.

All international passenger manifests have to be sent to APIS after boarding but prior to departure whether travelling from or to the US.

http://www.cbp.gov/linkhandler/cgov/...quirements.pdf