Have had 4 ORs up to this point, and its split 2-2 on if it truly matters. Current OR has said it doesn't matter.
The fact that they only really track 1st and 2nd on the dashboard indicates it is a factor, now it will vary. SWO for instance for the longest time would take people that were 3rd, then they put out a memo that said only 1st and 2nd would be considered for SWO, then that went away. Supply for the longest time rarely took anyone that wasn't 1st, same with IWC designators.
It could be a factor for SWO now but not supply, or vice versa, as it changes, I would say the greatest indicator is how many people on this site respond and say they were picked for their 3rd choice. That would be an interesting data point.
Aviation just cared about how good the scores were.