Grounding is great when GPA Mesh is used on the inside of a wall, with wiring behind it. The electric fields produced by normal wiring and other outside sources can then be led away by the GPA when grounded. You do not need grounding to make the shielding against radio frequency radiation work. That will work regardless if it is grounded or not.

When using GPA mesh on the outside of wall framing, the wiring is on the inside with you and so grounding wouldn’t help you with electric fields. It may still be desirable or required to be grounded is there is strong electric field sources on the outside of the structure, like solar panels or nearly local distribution power lines/transmission lines, OR if it’s required by law to be grounded. There is a small chance of electrocution if electricity makes its way onto the mesh (just like those metal insulation foils) and is not grounded. Grounding in that event would lead the current away to the ground connection and the circuit breaker or RCD would cut the power instantly. Therefor grounding is a good idea.