If the Test Button doesn't trip the GFI breaker then the breaker is either defective or not properly connected. That should be fixed immediately because it is the only thing you can count on to save you if you become the substitute for a proper grounding system. A properly installed GFI should trip when the test button is pushed no matter what else exists in the system.
Electrical items and metal parts larger than 4" in any dimension(680.26(B)), or that penetrate more than 1" into the pool shell, that are within 5 ft horizontally or 12 ft vertically above the pool should be connected with a #8 solid copper conductor, insulated or bare(680.26(C)). It is not required to be connected to the grounding system of the supply (See 680.26(A) Fine Print Note). However, if equipment such as a pump motor is properly grounded, and is properly connected to the "grid", then that equipment will all be tied to the system equipment ground.
If you have no grid but connect the metal parts, then I would not tear up concrete.