A study done at the University of London found that constant emailing and text-messaging reduces mental capability by an average of ten points on an IQ test (5 for women, 15 for men). This effect is similar to missing a night's sleep - or smoking cannabis. "Always on" is clearly not the most productive way to work.
Why?
When your brain is on 'alert' constantly it increases the allostatic load, which is a reading of stress hormones and other factors relating to a sense of threat. It creates an artificial sense of constant crisis. The fight or flight mechanism kicks in.
Given your small amount of working memory, you decrease the amount of data that can be held for what you want to focus on at any moment. So, whenever you multitask, accuracy does down.
So if you really want to innovate, turn off those notifications, put your phone down, close your laptop, put away the iPAD, clear your calendar - and create the space and time for deep thought. And if you want to read more about this, see recent work by David Rock, Mark Jung Beeman, and others.