This is the official explanation from Peugeot:

"In its "automated" version, which eliminates the need for a clutch pedal, it is an economical alternative to a traditional automatic gearbox with its two operating modes: manual or automatic. This responsive gearbox allows the driver to change gear at any time by operating the gear lever or “paddles” placed behind the steering wheel. It is intelligently controlled and can meet the expectations of those who prefer stress-free driving by changing gear on its own. In automated mode, the electronically-controlled gearbox improves fuel consumption compared to a traditional manual gearbox, thanks to the electronic management which chooses the optimum time to change gear."

So in short, yes you can leave it in automatic mode.