No, an RCD trips if there is sufficient imbalance in current (usually around 30mA) between live and neutral which is most likely to be lost via earth. If the earthing conductor is broken and there is a fault on a piece of equipment, the earthing path could be provided either by bonding (metal water and gas pipes should be bonded) or through someone or something touching it, which will cause the rcd to trip.
Remember if the RCD doesn't trip when you press the test button, something has gone wrong.
Adam
January 2010