As you mentioned, BN is a tie-breaker for same tier op-ups. ie. if they had to choose between 2 GOs, in normal circumstances, they'd choose the one with the smaller BN. So yes, many people do check in online right at 48 hrs to maximize their chances. It does not make a difference however, where you get your boarding pass. As I like to collect my BPs, I never print my own, and get them at check-in. I still get op-uped.