So my questions are: can one make this kind of a distinction? Is it desirable to keep these two kinds of sessions separate?
Nearly impossible to separate except if you listen to just a one or two instruments alone or concentrate on lead guitar lead vocalist. If you read up on "masking" then you will realize that what we hear is highly dependent on the balance of the frequencies heard and their precise timing.
Once you have a complex orchestral piece or an 11 piece jazz band then the quality of the system will often affect the presentation to such a degree that you cannot separate the two. Lead guitar and often lead vocalist is easy enough to evaluate on any system. However, at a deeper level, even simple things like decent bass response (very expensive to get accurate bass) may affect your ability to clearly distinguish bass guitar notes from kick drum.
Basically anywhere that two instruments interplay and share a fair amount of frequencies then it becomes system dependent - tuba/baritone sax, bassoon, double bass...in fact many instruments that form the rhythmical foundation of music require a system with good accurate bass. IMHO, the typical one note ported speaker with oodles of harmonic distortion coupled with typical room modal issues can make the critical listening task very difficult - right up to the lower mid range.
Midrange can also be a problem if it is "scooped" or laid back - as most 'accents' in music require a good forward midrange in order to correctly hear the emphasis from the musician. For example David Garibaldi is very well known for playing at several levels - this complex method of accenting drums (different from your rock n' roll back beat) is all too easily lost on a "scooped" mid range speaker.
Another issue is driver integration across a crossover - often a problem with speakers that have a crossover close to 1000 Hz (a critical listening frequency). Finally, impulse response is absolutely critical too...a speaker or amplifier that has odd ringing or resonance will cause masking too (in the same way a poor bass response does)