In either case, storytelling is a way of not being present. It's also a way of not taking full responsibility for how we engage in our present moment--storytelling is a way of putting things onto others or onto external circumstance ("people have hurt me;" "things will be better in a year").
And email plays into this. When I open my email, I often find that I am steeling myself for bad news or I am seeking external confirmation ("when, when, when will that journal editor get back to me;" "have I gotten into a conference," "oh, no, is there a student who is mad about his grade"). All of these are part of narratives about my failures and success, and all of them are external to me and the pleasure of daily work.
Though i am very undisciplined in this arena, it strikes me that making my writing time a time that is sacredly sealed off from emailing would be a very healthy thing--no emailing prior to writing, no email breaks during writing. If one aspect of maintaining a daily practice is finding pleasure in it for its own sake, then switching into the mode of looking for feedback that plays into my stories about acceptance and rejection would seem to be counterproductive.
The feelings of pleasure and responsibility that come from regular writing come from being in the present-time flow. They are the writer's own. That's my story and I'm sticking to it.