He 100% is the sort that would make reckless moves and grand gestures when it comes to romance. This is the lad who jumped out a window to get a super to leave her room. Damian is overly dramatic I can see him being a real Prince charming type.
I'm not sure if he's into Djinn romantically though. I know she likes him [as does Red Arrow] but he seems confused right now.
At 13 he's starting a little young.