Just wanted to chime in to say if I, as a regular passenger, heard a proposal over the PA it would make my day and make me smile. How can anyone say, "Ugh, keep your personal business to yourself." This is what? 3 sentences at most over a PA? Big deal.
That being said, just because this girl "likes airplanes" doesn't mean she wants to get proposed to on a plane. If it's a spur of the moment impulsive thing on his part well then..okay... but to plan the proposal for in flight...first class or not? Just don't see the romance in that.
Maybe this guy likes attention? I don't know. But if he can think of somewhere else to do it she may appreciate that.