No, they would not be equivalent.
Suppose you have a circuit in steady state, and somewhere in there it has a diode. It will have a current Id and a voltage drop Vd. You could replace it with a resistor with R=Vd/Id, and nothing would change in terms of the current node voltages and currents.
Is it an equivalent circuit? Of course not, because once the conditions change (e.g. different excitation, or time passes and a comparator changes state, etc.), the diode will behave differently (non-linearly) compared to a simple resistor.
A snapshot in time of the node voltages in a circuit is not enough to characterize it, or even to determine that it is equivalent to another circuit that happens to have the same node voltages.