I agree that it is good to get out of one's head with respect to the system when it comes to listening to music. Yet in order to deepen the emotional, visceral experience I like to engage with the music itself intellectually. I have found that this helps.
My favorite example, out of many possible ones, to explain why this is the case: If you do not intellectually recognize a variation of a melody as such, that is, in its relation to the original melody, how can you emotionally appreciate its beauty – as variation, not just as melody in itself?
Understanding of music thus can considerably heighten its emotional impact. The human experience is a whole. One cannot neatly compartmentalize it into 'rational' and 'emotional' parts. Attempts to do so miss out on the richness of life.
Well, yeah, but ... okay...
Can you read music Al and follow a score? That's a great way to have fun with the very example you mention.
I truly enjoy an intellectual understanding of music, knowing about intruments, knowing about the evolution of 'styles' from one composer or era to the next, trying to figure out different conductor's interpretations of the same piece, knowing about performers, and experiencing the act of performance and the skill involved in playing an instrument.
Imo, one doesn't need to intellectually recognize a variation of a melody in order to experience it and appreciate it within the context of the piece.
Ask a composer or performer if a listener needs to recognize a shift in the time signature from common to waltz in order to enjoy what they're hearing to the fullest extent. (If you're looking at the Copland quote, remember who he was.) I'm reluctant to gauge one person's personal enjoyment versus another's in terms of what they know when listening.
I don't think anyone (in this thread anyway) advocates compartmentalizing music understanding or enjoyment into this and that. I completely agree with you that intellectual engagement is satisfying and rewarding on many levels. And if that is what heightens one's personal "emotional, visceral experience " then by all means.