I used to write on a laptop that wasn't connected to the internet. It was a great way to ensure productivity, but it was more cumbersome when I had to do any research because I had to boot up a different machine. Now that we have WiFi at home, I have compressed to one laptop, which is connected to the web. It's easier on some ways. In my current WIP, part of the action takes place in the Lynnhaven area of Virginia Beach, where I used to live (before it was even part of Virginia Beach!). When I want to know what else is there or how far it is form on place to another, Google and Wikipedia between them have managed to answer all my questions. Since this is what I call intrinsic research— not the kind of factoid I can put in square brackets and say [find out later] but information needed to establish setting— in some ways, having the web available actually furthers productivity.
At the same time, seeing notices when I get an email is distracting. I might turn that feature off. Oh, wait, someone just sent me a message. Later, gator!