If you've finished the conversation, then that's it, right? Why continue small-talk if there's nothing interesting to talk about?
Usually if someone writes to me and asks me a question, I'll answer it. Sometimes I'll have a question to ask myself. Same vice versa; if I ask someone a question and get an answer, I'll tell them thanks, and I'll think to myself either, "this person is really cool for answering honestly" or "this person took what I was saying the wrong way" etc. When I have more questions, I don't think twice to PM them and ask again. But when the information requested has been transferred, why continue with mindless babble?
Then again, no, I haven't made any friends on this site that have turned into something where I meet the person in real life and go talk to them. There are people that I find friendly, and people I think positive thoughts about, but we don't hang out on weekends and grab a beer or anything.