There was one report here a few years ago that suggested that it does: Two couples purchased tickets plus EBCI on the same day. A few months later, one couple repriced their flight when the price went down, the other couple did not. The couple who did not reprice their flight got low A boarding passes. The couple who did reprice their flight were further back in the line. That suggested that when you reprice your flight, your EBCI purchase date gets updated to the date you repriced the flight, putting you further back in the queue.
There have been other (more recent) reports that people who purchased EBCI and later repriced their flights still got low A boarding positions. In these more recent reports I don't remember if there were others in the traveling party who purchased EBCI the same day but did not reprice so that we could compare boarding positions between the two groups.