Glued is an understatement! I kick off by live-tweeting the thing, so as to get the rest of the audience really involved. Once they take it and start running, I can then step off the tweeting and get more to monitoring and engaging - so its about taking the audience in the direction we think it best for all. I'll usually clear 2-300 tweets myself during the course of a single event day, in addition to monitoring everything on the hashtag. For our last major conference, we hit something like 17m impressions on that, so I think we're actually approaching the point where I need to add some smarter listening into the mix.
Worth noting - Twitter isn't just great for the content amplification, it's also good for logistics, complaint handling, information broadcast. It's the first place people will usually go to complain, so it's a great way to catch problems early - if you're listening closely enough!