I wish that worked. I'm in an open plan office where I constantly need the headphone to drown out the noise all the other things happening (people talking to each other, marketing people making phone calls, people walking about, etc) so that'd mean I'd be constantly unapproachable. I'd actually like that, but I'm pretty sure my co-workers and employer wouldn't.
A friend works in an office where headphones are even banned because they create too much of a barrier to talk to a co-worker. I'd go absolutely crazy there in less than a week.