I've known NFs who totally gave off the empathy vibe - it's amazing spending time with them, kind of like coming back to a warm fireplace after a day spent in the cold among strangers. But as far as many or all NFs doing this - it's difficult to say, because when they're not as warm it's harder to tell their type. I don't know if my NF friends ever saw their talent as leading to problems from people who take the connection too seriously - can't recall anyone mentioning that to me.
I'm about half F and sometimes I do get people telling me fairly personal things when there isn't a solid basis for that deep an interaction. I usually enjoy that kind of connection and reciprocate. Don't think anyone ever makes a big deal out of it afterward. There is the occasional oddball who starts spouting off randomly about his life and then asks me out, but that probably has little to do with my personality type and everything to do with his own issues. I can relate to the gooey heart thing though, it's very hard for me to walk away or cut someone off if they're telling me something intimate about themselves, even if I really want to leave (as in the aforementioned case with oddball).