No—on the Sony NEX-5N there isn’t a normal user-controlled way to leave the shutter closed when powering off.

The camera keeps the shutter open during live view, focusing, and metering. When you take a photo, the shutter closes, opens for the exposure, then closes again briefly while the sensor is read out, and finally reopens for live view. So if you happened to receive the camera with the shutter closed, that was likely just the state it was left in, not a feature you can reliably reproduce.

It’s also not a good idea to treat the shutter as a protective cover. Camera shutters are delicate precision parts, and using them like a lens cap increases the risk of damage. Use a proper body cap or lens cap to protect the sensor and mount instead.