My own dismaying experience with Inbox Zero was that becoming hyper-efficient at processing email meant I ended up getting more email: after all, it’s often the case that replying to a message generates a reply to that reply, and so on. (By contrast, negligent emailers often discover that forgetting to reply brings certain advantages: people find alternative solutions to the problems they were nagging you to solve, or the looming crisis they were emailing about never occurs.)
I do try to get back to people as quickly as I can, even with just a word like "busy". But I also have noticed the above effect - when I am out of cell range, people seem to find solutions without me. And in my hyper-productive-stupidity mode I feel chagrined - 'left out', often.
Will do better to 'let go' in '17. Smartphones are making us all psychotic.