http://www.delta.com/traveling_checkin/ticket_changes_refunds/sameday_travel_changes/index.jsp
Annecdotally, a recent flight on DL SFO-ATL-LGA resulted in our checked bags arriving on an earlier flight than we did. They were sitting off to the side by the baggage office and took awhile to find. So, even though they were tagged correctly, they didn't end up on our plane (somewhere along the way).
Calling DL is best, but even then I wouldn't rely on their answer. IIRC, there aren't confirmed day-of changes for the nominal fee on international itins; such changes result in a re-fare/re-issue situation....
Safe travels!
Pat