This seems like trying to understand how a car engine works by listening to the pitch of the sound it makes. Sure you can deduce somethings, but you aren't really going to understand the engine.
I'd say, quite much. I'm sure there would be no problem to figure out at least a few layers of memory, the existence of a separate GPU, the fact that it has a limited capability of concurrent computation and that most computation occurs at a very minor part of the CPU etc. Then, if we also figured out that the CPU is based on a lot of small transistors that'd probably give some insight as well.
But this would obviously not be nearly enough to build our own computer with capabilities similar to a modern computer. That'd require a lot more detailed knowledge and advanced equipment
I'd say neuroscience is somewhere at the beginning of the mapping process, certainly not nearly enough to construct our own brain, but still very informative on the subject of how the brain functions.