ADE7758 Power supply design
As a bare minimum the neutral needs to tie into the ground of the Metering Chip because of the need for the chip to also connect to the AC line hot side for the AC voltage monitoring. See circled areas in the diagram below. Without it the voltage measurement would be like trying to use a digital multimeter with just one lead.



Picture Source (page 12)

Note that the reference board power supply showing connections of both sides of the transformer to the same side of the AC line is an unfortunate documentation error.

In many situations this type circuitry may very well have its power supply directly derived from the AC line without using the transformer coupled linear 7805 design used for the reference board. 

In a single phase design the circuit would work just fine if the HOT and NEUTRAL were swapped. The product packaging and usage would have to take care of the safety aspects of this. On a three phase design on the other hand the NEUTRAL connection must be properly comprehended versus the three phase lines. Once again safety considerations are extremely important. 

Final note: When working with any line attached circuitry at the design and engineering stage great care needs to taken to stay safe and not make any stupid mistakes.