Yes and no.
Yes, we can always measure. Is that what we hear? Not necessarily.
Neurological: we don't know how we listen. While we are at point we can recognize with decent accuracy what people listen to through fMRI (
https://www.the-scientist.com/the-s...als-which-songs-people-are-listening-to-30321) we still don't understand how our brain processes sound. My inner violin does not match someone else's violin. Some progress is being made, some of it very very cool (
https://www.ncbi.nlm.nih.gov/pubmed/30696881) but that remains very far from a deep understanding. The fact that we all hear differently is well established (for example
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4757893/). A lot of what we hear is actually not heard but reconstructed by our brain from a sparse signal: this is why we can recognize a violin from an amazingly poor recording and reproduction device or why we are so good at isolating human voices in a sea of noise. Anecdotally, I spent some time listening to vocal performances with a pro opera singer and teacher last year: while the signal that reached our hears was definitely the same, our perception of it could not have been more different. Where I perceived some guys singing together, she perceived and classified five persons, each with their own characteristics.
One important thing to note is that this extremely high level of subjectivity, which is often exploited by "golden ears" reviewers or marketing, does not prove that cables can make a difference
, it simply means that confronted with the same signal different brains hear different things.
As far as recovering individual instruments from a symphonic piece (or even much simpler ones), there are many obstacles in terms of
information theory: even if we could perfectly define identifying characteristics for each instrument, we quickly reach a point where the information simply isn't there in sufficient quantity in a recording either in real time or even in the totality of the recording. When a conductor isolates an issue with a musician/instrument in his orchestra he dynamically re-allocates his brain bandwidth first to the problematic area, then the musician. We can't do that on recorded music as it stands. That could, by the way, be an argument for extremely high data rate recordings in the future - listening to a symphonic orchestra and being able to zoom on specific parts would be very cool, in a computational photography kind of way.
computational complexity: even if we could perfectly define identifying characteristics, computing the interactions of instruments and the resulting sound waves may be impossible, asymptotic complexity, unsolved P=NP kind of stuff, etc... Note that it is the computing of the result of 100 instruments together that is in that class of difficulty, doing the reverse operation can be proven to be impossible (see information theory caveat above) in some cases and, even if it is doable (say a couple of instruments in a simple set up) it is still much more complex than the direct problem and we fall back in the computational complexity. Also worth noting is that when it can be achieved (at least perceptually) there is a whole lot of reconstruction in the background. If a violin and piano play together, are perfectly identified, there will still be overlapping information that can't be assigned to one or the other: a model is used to fill the holes, which is - at least from a result point of view - similar to how our brain works.
One of the fun aspects of the field is that currently researchers are trying tons of trendy "AI" algorithms to advance our understanding of how the brain works. Where one could naively expect something like "our brain is doing that let's try it in software" the reality is "hey, my clever algorithm delivers decent results, that could be how our brain works"...
One easily available document is "Automatic musical instrument recognition from polyphonic music audio signals"
(
http://mtg.upf.edu/system/files/publications/ffuhrmann_PhDthesis.pdf) - a good resource with plenty of references.
Ultimately, while I am 100% in the camp of the people who say that a cable (or else) with no measurable impact on the signal can't change the signal that reaches our ears and therefore is snake oil they are over extending themselves by generalizing radically.
A system can be 100% deterministic but remain essentially non predictable.
