Why wouldn't it? It wouldn't be exactly the same, but the important information is there. Does it matter if it's slightly off?
Consider that your real brain is influenced by tons of random factors and meaningless information. If a protein drifts to a slightly different location maybe it could slightly affect the output of that neuron. But if just assume that it is where it is supposed to be for the purposes of the simulation, it should be fine.
It's not like something like that encodes any important information or has anything to do with the algorithm that your brain is running.
1. We're limited by our own models of physics. We can only record what we know about. That's a pretty significant issue when you're trying to simulate physics.
2. In physics, we can run an experiment over and over again so as to refine our model. We isolate systems and try to study simple interactions. When you study gases, for example, I think you will find that things are modeled statistically. We record details to the extent that they help with our model.
What I'm wondering is how we would do this with biological systems. Can you run the "experiment" over and over to try and understand the "right way" this biological system was supposed to behave? Is there a "right" biological system? How do you know what the relevant biological (sub)systems are? How do you identify what's important? How do you abstract? What's a "good enough" replica?
What I'm trying to get at is that I don't think there is a good layer of abstraction for biological systems. I think the physics is the only good layer of abstractions. But...
3. If we had to record states of molecules, for example, then making a digital copy of everyone seems really not feasible. It doesn't seem feasible because of memory or computation.
I think you could abstract to the individual neurons or maybe the different parts of the neuron. It doesn't matter that you don't have an exact physical simulation of every atom.
Consider that your real brain is influenced by tons of random factors and meaningless information. If a protein drifts to a slightly different location maybe it could slightly affect the output of that neuron. But if just assume that it is where it is supposed to be for the purposes of the simulation, it should be fine.
It's not like something like that encodes any important information or has anything to do with the algorithm that your brain is running.