Can Neutral terminal stay connected to a power supply and Live terminal switched?
Is it safe/functional to keep the Earth and Neutral terminals connected from the power supply to the AC/DC converted while switching on and off the Live wire?


Yes. Not only is this safe, but it's the standard.

Switching neutral is dangerous: if the live side of the switch fails closed, parts of the device may be energized to line voltage while the device is switched off. If the device is plugged into other powered devices, it may even end up powering itself through the other device's ground.