Yes and no. It can happen that way, but only with a very mature process node which has had its functional and parametric yields optimized to a tight(er) distribution. Which in general is where all process nodes end up once they have been in the hands of the fab engineers for 6-8 quarters, if not sooner.
Okay, hold on - your original statement was that the chips will use similar power consumption when operated at the same frequency, voltage, and temperature. So the coefficients in the dynamic and static power consumption equations will be close to the same.
But SOFTengCOMPelec was making a much stronger statement, that the chips will have the same frequency/voltage curves, max frequency and voltage and so on. When is this ever really true even with a mature process? If this were the case Haswell, for example, they would all overclock the same under the same parameters, when in practice there's a pretty huge amount of variation.
Same thing with mobile SoCs, if you look in kernel source you can see tons of different bins describing separate voltage/frequency curves.