This feature would be super helpful for my research if available! +1
As @thom_nic mentioned, the in_reply_to_status_id field can be used as a work around to re-construct a conversation. For any tweets with this field, we can (1) find the tweet this current one is reply to, then go to that tweet to check whether that one has a in_reply_to_status_id field, and continue this step. (2) Search the entire collection of tweets to find whether there exists a tweet with a in_reply_to_status_id that match this current tweet. Do this step for every tweet involved in the conversation.
However, this could work only when you have a relatively small collection of tweets already downloaded for research purpose, since it may take a lot of time searching through for real-time applications. But an advantage of real-time application is that you can just do step(1) for each incoming tweet.
In addition, since API only gives a sample of all tweets, there might be a lot of broken point when trying to re-construct the conversation (I have not tried yet to see how much broken points there can be). Would really appreciate if Twitter API could support the conversation feature including how many conversations a user has engaged in and the length of each conversation.