I see what you mean and I've thought about that scenario in "romantic" comedies too.
But as many things, it depends. It depends on the people involved and the context.
So, for example, if a guy goes to the "romantic" extreme of chasing after the girl before the plane leaves, if the girl has been with him for a long time, and knows him well, even if she is no longer receptive of his love, that doesn't mean she will consider him a stalker or desperate.
She will probably think it's romantic, and recognize that, but she will tell him that unfortunately she feels that their love can no longer be. Also, the girl would have to be somewhat sensitive to the guy.
If she was more insensitive, she might just tell him to drop dead, viewing him as neither romantic nor desperate, nor a combination of both, but as some asshole she just wants to get away from.
If on the other hand this is a guy she barely knows and who she has just let down, who goes to this extreme, when it seems "uncalled" for (seeing as there is not much history there to fight for, in a sense), then she will definitely not view it as romantic, but instead as desperate and stalker-like.
If she is a nice girl, she might be willing to think that though he meant well, he was misguided and might need help...
Of course, if it all works out, the gesture becomes automatically more romantic because she has accepted to give it another try.
I'm not sure what I'm trying to say here, except it seems to be apparent that if the effort made to reconnect matches the common history/depth of the bond of the couple, then it is more likely for there to be a romantic outcome.
Also, even if the guy is rejected, the outcome can be perceived as a romantic effort that sadly didn't work out, depending on how the girl reacts to him.
But to me, this gesture, does not come off instantly as romantic. I'd first say it's brave of the guy to just throw caution to the wind and go after what he wants. I think it's not a bad thing, getting rid of all masks and just saying things clearly. And then, it can become romantic, depending on what is said/done.
Commenting on your statement of what is romantic:
to me: A show of affection that doesn't fit under "normal" circumstances.
twist: and is accepted by the recipient, perhaps reciprocated, leading to a romantic evening.
Like Manic-Skafe, the idea of normalcy doesn't seem to make sense here.
I'd rather say it's a show of affection for someone you love (romantically that is, heh), and that involves an implicit or explicit declaration of "romantic" love, where the person showing affection expects nothing in return except to see the other person happy.
Also, I disagree that it has to be reciprocated, even if it is not, there was still a romantic effort involved. Though it's nice when it does lead to that romantic evening you mention
