Per SWA..
"If an EarlyBird Check-In Customer chooses to change a flight, will the EarlyBird Check-In options transfer to the new flight?
It depends. EarlyBird Check-In is tied to the Customer’s reservation for which the EarlyBird Check-In purchase was made and will be transferred to the Customer’s new flight if he/she changes the flight at least 25 hours prior to the original flight’s scheduled departure time and so long as the change is to a flight that will depart in more than 25 hours. Since EarlyBird Check-In is associated with a reservation, any changes must be made within the same reservation record (same confirmation number) in which the Customer purchased EarlyBird Check-In."
Broken down yes you can change flights, but it must be 25 hours before your original flight and 25 hours before the new flight is scheduled to depart otherwise the system will just default you to the general check-in que.