What is the exact function of the board?
Generally if the power supply to the board is isolated, i.e battery or mains supply that is galvanically isolated, then if this design is not stand alone but integrating with other systems there can be an advantage to earth grounding, it all depends on what type of external influences there may be on the board such as interfacing with noise creating circuits.
If a stand alone application then there is probably no need to earth ground, but this does not affect the ground plane which is usually the supply common or GND.
The board function is one main criteria.
Max.