I know it plays a bit of a role in PSO 1&2, but I've always wondered in Ep. III if it has any impact at all and if it affects the run in any other way.

Sorry for the extremely late reply! Section IDs may have a small drop rate % influence on different types of cards, but they do not prevent you from opening any certain cards. Full research hasn't been done compared to Ep1&2, where each enemy only has one rare drop and can be nailed down.