In my view SEQ is simply check-in sequence. Common across may/all carriers. I have had conducted OLCI at the earliest point and had very low SEQ numbers, unrelated to surname position in alphabet.

The SEQ number allocated might also be influenced if a flight is a second sector; ie a pax checked-in from LHR-HKG-AKL might see that pax with a lower SEQ number than someone flying only HKG-AKL who does OLCI as soon as it opens.