However, my contention is that the material constraints of how those processes are embodied are going to have a significant effect on how the system works

Sure, but that's no basis to think that a group of logic gates could not eventually be made to emulate a neuron. The neuron has a finite number of things it can do because of the same material constraints, and while one would probably end up larger than the other, increasing the physical distances between the thinking parts, that would surely only limit the speed of an emulated thought rather than its substance?