This is obviously going to depend on the site/service/salesperson. But most sites I've come across don't pop-up a live-chat invitation. So if you find it annoying, you could always not go that route. Or some businesses prefer to use live analytics to identify when a user who's shown interest in a product is looking for some help—then, and only then, do they pop-up a live chat invitation.
Anyway, I haven't used Live Chat on any of my sites yet, but I've been evaluating different options. You may find my question helpful.
I think adding a new channel for communication between you and the customer can only be a good thing. Sometimes email isn't fast enough but the visitor isn't interested enough to pick up the phone. A live chat sales rep is right there on the site, removing any barrier to contact. Think about it: how often have you had a question for a service provider or manufacturer while browsing their site, but were too lazy to write an email or pick up the phone. It's so much effort to look up the appropriate e-mail contact, open up your email client (or log into Gmail), and then type up an e-mail that probably won't be answered for at least an hour. Looking up a phone number, dialing, clawing through voice menus, and being put on hold while waiting for a phone rep to become available is an equally unpalatable proposition. A live chat representative, OTOH, is just one click away. Don't ever underestimate the power of human laziness...
It's also cheaper to have live chat customer service reps than phone reps—especially if you can get a live chat setup that supports 2-3 operators, each of whom can manage 2-3 conversations at a time, for less than the cost of setting up 4-9 phone lines. So if you're running a business that is mostly conducted over the internet, then this might be a preferable support option (you could type links or even display images or multimedia in the chat), or at least another alternative for real-time communication.
You could even have a system that's interfaced with SMS (could probably be done through twitter) so that your chat reps would be able to answer chat requests even while they're out.
And if you have a live chat solution that also comes with video conferencing/1-to-1 capabilities, then it adds another level of intimacy and interaction that could greatly improve your conversation rates over plain old e-mail or phone.