Why is supply noise a problem?
What does a milliohmmeter measure? Resistance. What is resistance?
Resistance is defined by the ratio of voltage across a component, to the current through it:
V = I*R
If we have noise in V, we have an exactly* proportionate noise in I. If we are measuring both, we have lost no signal (information about R) except when V and I go to zero**, which happens only rarely.
*Minus Johnson noise, which adds a noise voltage in series with the resistor, corresponding to its resistance and temperature. This voltage is unknown, so introduces the same error in Vmeasured. Or the Norton equivalent, and the proportional error in Imeasured, same thing.
**Close enough to zero for the purposes of the circuit, anyway. Example: the least LSBs of your ADC, around whatever the zero or reference value is.
DC is itself a vulnerable method: there are many sources of small DC voltages, like thermocouples. These can be swamped to some extent by using a larger excitation signal, or they can be nulled by using AC and filtering DC out of the measured signal entirely.
AC likewise has some drawbacks, because even at low frequencies, reactance is nonzero, and may be nonzero enough to matter. We could address this with a properly phased detector (so we only measure the in-phase component: the resistance), or say by measuring at very low frequencies to begin with, or a selection of frequencies so we can analyze if the response is stable or not.
In a sense, noise is the perfect stimulus, because it has all frequencies at once, and by measuring the source and the response, we can solve for everything at once (I mean, given unlimited computing power and cleverness -- in this case, a Fourier transform would serve nicely). You probably wouldn't want to bother going to such length, as there are easier signals that will do very nearly just as well -- just that you could.
The other thing: it would be nice to measure only voltage (or only current, but almost nothing measures current directly). Which means we need another resistor, to convert current back into voltage. Thus, we would have a resistance bridge, or at least a half bridge (a divider).
Best part about using an ADC in this way: the VREF doesn't matter either, it can be relatively noisy and indeterminate. As long as it gives an acceptable result, you're fine. All you are doing, is comparing the ratio of resistors, to the ratio of ADC steps. The exact voltage is unimportant!
Tim