You said you had your doubts about the accuracy of a reading resistance between the ground and neutral with the power on. The point is that it will not materially change the result because there is no material current flow between ground and neutral. I = 0, therefore V=0.
That's not actually correct. N and G are bonded at the service disconnect and should not be bonded anywhere else (although they sometimes are by mistake). So obviously N and G have the same voltage at that bond point (it's a single point). Call that bond point the 0 voltage point.
Then if you check the voltage at any other point on G, it should be 0 volts, as there should be no current flowing on G.
But if you check the voltage on any other point on N, it will be non-zero if there is any current flowing on N between there and the bond point. Because the conductors aren't superconductors, so they have some resistance, and V = IR, so there is some voltage change along the length of the conductor.
So say you are measuring voltage N to G on a receptacle, and there's 50 feet of #12 AWG between that N receptacle terminal and our 0V reference point, and upstream of that receptacle loads are drawing 10A, and downstream of that receptacle the current stays 10A, no additional loads. #12 copper has a resistance of about 2 ohms/kft, so that 50 ft #12 neutral conductor has a resistance of 100 milliohms. With 10A of current on it, the N at the receptacle will be at 1V relative to our 0 point. So if you measure the voltage between N and G at that receptacle, you should get 1V on your DMM.
Now why is that relevant to resistance measurements? If the power is off, and you measure the resistance between N and G at that receptacle, you should get 200 milliohms (double because of the two conductors, N and G). That's high enough I bet many cheap DMM will read it, although I don't really know what typical DMM specs are.
So how does the DMM come up with 200 milliohms? Per Mongo's information, it might inject 0.2 mA DC between the probes, and measures the voltage difference, which will be 40 uV DC. Assuming it can distinguish that from 0V, it will report the imputed resistance.
And what happens if you try that with the power on and 10A AC flowing on the neutral conductor? Now the DMM will be seeing a 1V AC signal with a superimposed 40 uV DC offset. I don't know what typical DMMs will do in that situation. 1V (RMS) AC between the probes might be enough to damage the DMM. Or it may not be able to distinguish the 40 uV DC offset from the 1V AC signal and give the wrong answer. Or maybe it can filter out the 1V AC signal and just see the 40 uV DC offset, and still give the correct 200 milliohm reading (or 0 ohms if that's below the DMM measurement resolution).
So unless you can offer us some further insight about how a typical DMM works internally, and how it will react to seeing that 1V AC signal with 40 uV DC offset, I don't believe you are in a position to contradict the typical DMM manual's instructions not to measure resistance while the circuit is powered.
Cheers, Wayne