And that is where I let the player decide to role-play. I have seen players wrestle with what they think their character would do, based on stats, or flaws, or whatever. But unless there is some form of compulsion, I am cool with them playing it their way. I really prefer to let them choose. But I make sure there are ramifications of one sort or another.
In your example, if he succumbs, then maybe she becomes a nuisance, or is going to blackmail him, or something. If he resists, then maybe she becomes a nemesis, or, and this is really good if the character cares for the NPC, but "Not in that way," she then falls for someone the PC is opposed to. Or maybe for either choice, there are no ramifications… but it is more fun to torment them a bit, don't you think?
If its added to the game it will be good that the Dungeon Master can use it as an odd experience in a certain situation. For instance is it a distraction and you miss a clue or you see your significant other in trouble and give your life to save her / him?
I find that a bit of romance adds to even the grittiest of combat games, so long as it is done with a bit of taste and realism. The only hard rule I have about such in my games is "Don't let it detract from the experience of others."
Fall in love with another player, marry the NPC you spent the past month escorting to his home, heck go and seduce the dragoness into not burning down the town and have a torrid affair with the same. Just don't expect me to put other players on hold while you do so.
A little romance can go a long way if its kept in a short post but having it extend over pages or hours can be a bit much because it starts to get old.
Yes a long drawn out romance can be good and it can be bad depending on how it is played out. A lot of people may not want to see all the mushy stuff so that can be hinted at or glossed over.
One of the problems with romance in role-playing is people trying too hard too fast. It should start simply and go with the flow of the game rather than a stop, jerk and then move to the next chapter kind of thing. Real romances aren't like that and they are not exclusively that way either. People get to know each other in the process of doing something other than getting to know each other.