Originally Posted by The Joker
Not really. Alfred was leaving because Bruce became Batman again. He revealed the truth about Rachel's letter in a desperate attempt to make Bruce see sense. Alfred was going to leave either way.
Either way, it's used as a last attempt to snap Bruce out of his funk and even if Alfred hadn't decided to leave at that point, Bruce's feelings are pretty clear and he probably would've wanted him out after that anyway. You could also argue that on a subtextual level, knowing that the feelings weren't mutual with Rachel ultimately served to help Bruce move on from her.
Just not buying that argument that this was only a superficial callback. It was a huge beat in the film, bigger than I thought it'd be even.