Yes! Home is just not a place that gets talked about much at all, though if pressed by anyone else, Hajime might mention that they used to live across the street from each other.

And if he sees any other guys talking to her in a way that makes him suspicious of the other guy's intentions, he may take them out behind the school for a friendly little chat of some sort. Said chat in no way involves anyone getting a black eye or anything. Just looking out for his friend, after all. Maybe he'll figure out that he should really ask her to prom next time it rolls around.