If there is no utility company grounding rod for electricity to complete a circuit, can electricity still flow to the earth, i.e. the earth (planet) being some kind of sink hole.
This would mean no circuit is completed however.
If the answer is no, does that mean a person could hold a live wire - again with no utility grounding rod - while touching the earth and nothing would happen - no injury/death?
there is no utility company grounding rod for electricity to complete a circuit.
The ground rod is not used to complete a circuit.
All electric circuits will function as long as the current leaving the source goes through the load and back to the source, whether the ground (earth) is connected or not.
The ground rod is used to bring the earth-local potential to exposed metal parts of appliances that are equipped to attach to the ground distribution. This brings the voltage difference between hands and feet to a safe value close to zero.
can electricity still flow to the earth, i.e. the earth (planet) being some kind of sink hole
There is always a capacitance between two conducting objects that will allow current. It may be small (even insignificant) but it still exists.
The planet earth is not an electrical "sink hole". If the earth is used like a wire to complete a circuit as much charge flows out of ground as into it. The bell current in the original telephones used this technique.
(this would mean no circuit is completed however)
No. If this were true, no battery operated device would function. Circuit comes from circle. As much current leaving a battery to power a device must return to the battery whether the device is grounded (earthed) or not.
does that mean a person could hold a live wire - again with no utility grounding rod - while touching the earth and nothing would happen - no injury/death
Speculatively, in general this might be true. Specifically I need to measure the voltage before touching. As the voltage goes up unsuspected current paths can bite. Don't touch a live wire! If you do and get hurt, Don't blame me. It all on you.
Utility electricity is always ground-referenced. It would be far too dangerous if it were left floating: if someone then accidentally grounded the live wire, neutral would become live instead and no circuit breakers would be triggered.
Grabbing a live wire at household voltages (limited to 240V) tends to be inconspicuous when you are wearing shoes with plastic soles and not touching anything else (smart guy that I am, I once demonstrated the harmlessness of touching a half-live TV chassis while holding a grounded lamp in the other hand: the "one hand in a pocket" rule could have prevented that). Brushing it will tingle due to capacitive currents.
At any rate, any sentence revolving around "you could touch a live wire" tends to revolve around a bad idea, one that increases the likelihood of killing yourself accidentally.
Heck, I even remember a Faraday cage demonstration in university where the professor did not get a volunteer and went in himself while still wearing a wired lapel microphone. Didn't make finding volunteers easier...
