It really depends on the style of conversation. It's not unusual on some forums to use the quote block (linking to the the comment being replied to) but leave it completely empty to respond to the whole comment. people can click the link to see the context, but don't have to re-read the whole thing again if they're following the conversation already.
On the other hand, quoting individual lines to comment on a specific section happens plenty too.
If the quote doesn't automatically give you a back-link, it can still be a pain to get more context. If it does, then that's probably passable but it still might be a few hops to get back to the start of a discussion and you don't get it all on one page (in a traditional flat system) if there is much activity at all. Twitter may be able to do better with a loose grouping in of related tweets (which should include all tweets being replied to) while still preserving some semblance of a flat system, but I don't know if they do - I don't use twitter extensively. I do know that I've found it sometimes difficult to figure out what is in response to what in the little I have used it, though, so I am skeptical.
On the other hand, quoting individual lines to comment on a specific section happens plenty too.