No.
"... on a 3 wire outlet, from the green case ground post to the
silver white neutral post"
* DOES NOT HAVE *
" ... the same potential as the bare copper safety wire has from
the green case ground post to the neutral binding posts in the
breaker box panel."
As posted earlier, the white wire and bare copper wire are
(essentially) same potential where they meet at breaker box -
the single point safety ground. Both wires have different
potential at their other (receptacle) end. That voltage
difference can even be measured with a digital volt meter when
the outlet is supporting a heavy load.

How 'different' at the far end? That answer first required
numbers - electrical parameters. Difference may be so slight
as to be unmeasureable or difference so great as to be a human
safety threat. But two wires with a common connection at one
end are not same (electrically speaking) as the other end.

Again, wire (even a superconductor wire) is an electronic
component - not a perfect conductor. Electricity at one end
of a wire is not same as at other end. To calculate the
difference, one must first apply numbers. But this difference
between two ends of any wire is why white wire cannot perform
the function of both white neutral and bare copper safety
ground. White wire and bare copper wire are wired so that
each conducts different electricity from different parts of
the same appliance. Both wires must remain separated so that
both wires conduct their electrically unique currents to the
same single point safety ground.

Do the experiment as posted previously. Connect a heavy
load to wall receptacle. Measure the AC voltage difference
between outlet safety ground and outlet neutral wire. Each
wire at the receptacle end have different potentials. 3.5
digit multimeters being so inexpensive and so ubiquitous that
anyone with a basic tool box has that meter - and can perform
this experiment.

If an outlet is drawing 20 amps, then everything in the
circuit is conducting 20 amps. BUT, the voltage (the
potential) between two wires is different at different
locations on the wire. Move one foot down a wire and the
voltage changes. Again, electricity even on one end of a one
foot wire is different at the other end. Difference may or
may not be measurable. But the difference always exists ...
because wire is another electronic component just like
resistors, capacitors, and inductors.

Rodney Kelp wrote:
Ok, For those who worry, I am NOT wiring a house like this. This is
only theoretical.
So from what you say I see that the short jumper, on a 3 wire outlet,
from the green case ground post to the silver white neutral post has
the same potential as the bare copper safety wire has from the green
case ground post to the neutral binding posts in the breaker box
panel. . Barring all possible disasters Is there any electrical
difference that the outlet sees where you plug things in?
If the outlet is drawing 20 amps then isn't it felt at the breaker
box paned neutral connection where the equipment ground is connected?
As a matter of fact isn't the bare copper safety wire seeing the
entire house current at that neurtal connection in the breaker box
panel at the outlet's safety ground?