"Can you approximate the circuit to this-? (assuming steady state, DC load)"
Can the earth be approximated by a football? Sure! if you just want to show that it is round.
How you need to model something always depends on what you need to use the model for. Really the circuit you have shown does not approximate the rectified 3-phase AC very well, at least not in the time or the frequency domain, because what you have after the rectifier is not a steady DC but a pulsing DC. However if you need to look at the average conditions (which you sometimes do) then I guess you could use that circuit approximation. In this case calculating the (derived) output resistance after the rectifier is fairly straight forward; you need to calculate the RMS voltage across and RMS current through the load over a full period of the AC and you need to know the theoretical AC voltage before the output impedance. Then the output impedance can be calculated as simply Zo=(Vac-Vrms)/Irms , where Vac is the theoretical AC voltage before the output impedance, Vrms is the RMS voltage across the load and Irms is the RMS current through the load over a full AC period. RMS is an abbreviation of "Root-Mean-Squared" and what you do is literally that you square your function (in the time domain), then take the average over time (integrate) and then take the square root of that. Of cause in order to do this you first need to come up with a function which describes the pulsed DC after the rectifier over a full period of the AC, there is a good bit of math-fun there for you to sink your teeth into. This is one of the first things you usually spend time solving equations for when doing an EE degre ;).
"How would R_G relate to the resistance measured when you place a multimeter between the generator pins R, B, Y ? (e.g. resistance between R and B, resistance between B and Y etc.)"
It would not relate at all (: the resistance you would measure would be completely different, and would depend on your measurement technique, especially as you have diodes in the circuit.