As confusing as it seems, a ground rod, or a water pipe bond/ground, has NOTHING to do with the third round hole in a receptacle. NOR does it have to do with the bare wire run in the wiring with the circuits.
The safety ground in your home, the one that "grounds" that center hole, comes from the neutral to ground bond in the main panel. That's IT.
To answer your question, NO that is not enough. A supplemental ground rod is also required along with your water pipe grounding electrode.
This may come right off the same wire as the water pipe though. Check that.