Since no one else has really said it explicitly, just do whatever you think the players want as long as that's okay with you.

For me, I usually don't allow any serious romance role play in my games because it makes me uncomfortable as DM and I know some of my players feel the same way. When the one guy in my group that always tries to seduce women in-game does that, I will just have a quick yes/no for him. My group plays to pretend we're fighting monsters, not pretend we're lovers whispering to each other.

If your table wants to all go down the road of a serious romance and you do to, then go for it.