Yes. Not only that, each separate grounding wire connected to the building’s steel work and plumbing should terminate at a single point connected to the dirt.
I am tempted to jump in here but there has been a lot discussed already and much of it is slightly off target. To begin with, no one is using the correct NEC terminology. There is a grounded conductor and a grounding conductor. The grounded conductor is commonly (and incorrectly) referred to as the neutral. It and the grounding (safety ground) conductor are connected together at ONE POINT only. That point is in the main service panel where the electrical service enters the building. All subsequent sub-panels (and there can be many of them) do not have the grounded and grounding conductors bonded together. This is very important in an outbuilding where there is bound to be a sub- panel.
The driven ground rods are 10’ by code and often a group of three several feet apart. The resistance from the ground rods and the earth should be measured and additional ground rods driven until a certain value is met. Very few single family homes have done this.
A large building will have a ring of heavy wire buried all around the building to serve as the ground. Even the re-bar in the concrete is attached to it.