In a word: NO.
Most single phase transformers are fed by two "hots" on the high side, much as we power a water heater.
On the low side, there are three connections. Two are the 'hots' to your house. The third (or middle) one is your neutral. It's the bare wire that supports the other wires on their way to your house. This wire is also grounded at the pole. Once it gets to the first overcurrent device at your house, it is grounded again (through the ground rod).
Look at the power lines. Typically, you will see two wires WAY up high, one lower down .... then, at transformer level, you will see two more wires. Finally, there will be some wires even lower down.
The top wires are the high-voltage feeds. That single wire below them is the neutral for the high voltage side (if there is one). The wires at transformer level are the hots from the low voltage side. Next down is the neutral from the low side. Finally, lowest of all, are the phone and cable wires sharing the poles.
What does the ground wire do? Who really knows? Dirt, even moist, "conductive" earth, is a rotten conductor ... especially when compared to a real wire. Some modern countries get along just fine without earth grounding.
The ground rod certainly does NOT help breakers trip under fault loads. Ground rods are allowed 25 ohms of resistance ..... A dead short to earth would draw less than 5 amps (120/25).
Older / obsolete distribution systems tried to use the earth as a conductor. Most of these utilities are locally owned. These are the places where, because of the resistance of the dirt, we have "stray voltage" problems.
A second cause of 'stray voltage' problems as ungrounded systems, where there is a fault between one leg and ground. When there are multiple high resistance faults (say, through lighting ballasts), there will be current flowing through anything conductive.
