With Gmail smart labels and some additional filters, most of the email that reaches my inbox actually requires my attention at some point. But often I'm in a talk or a meeting. I've trained myself to ignore the buzz of my phone and now I can see I have to ignore the buzz of my watch as well--harder to do.
Our lives just get more interconnected. Some people I hear purposely disconnect themselves to get work done. I like to deal with issues as they arise and not let them pile up. But the trick is to remember that when you are in the midst of doing something best to ignore the interrupt than act upon it.