Not for me.
You can right all the paragraphs you want, but they will not change my experience.
Rayforce in my opinion is an example of a game where the beautiful music and mute sprite puppet show of a story brilliantly work with the excellent gameplay. But would the gameplay be any less enjoyable for me if I was playing with the music muted, or if the beautiful sprite artwork was removed? Nope. I LOVE the gameplay, and the rest of the elements are just a bonus.
There is an emotional connection thanks to these other elements, yes. But there is also an emotional (maybe) connection and stimulation from the gameplay itself, which would not be diminished in the slightest if the audio, visual, and lore elements of the game were removed.
Would the game technically be "greater" in a 2 > 1 kind of way with the addition of story, art, and music? Yes. But is the gameplay itself "greater" because of these elements? No. 1 still = 1. Story, art, and music are not added to that sum, even though they add to the sum of the games content and value itself.
Similarly, if you took out all the quirky art in Skullgirls, and replaced all the sprites with stick figures, I would still find the gameplay exactly as satisfying.
If, in megaman, they simply listed the stage names instead of giving you a level select screen with each of the robot master's faces on them, and took out the part where the robot master poses after you select his stage, wouldn't the boss battle at the end feel almost inconsequential? Like that was just kind of some guy at the end of the level that tried to kill you?
Bro, I've played a thousand shmups where the bosses at the end were either faceless generic machines or generic loli's, and those battles were still more fun and exciting then any Mega Man robot master.
Allow me to sum up my opinion again:
Art, gameplay, music, story, all create different kinds of pleasure. When they compliment eachother, it creates a new kind of feeling (relating to the AESTHETIC, which is also separate from gameplay), but does not change the base "value" of any individual element. In essence, what you are talking about is using the interrelation of elements of a game to add
additional emotions to the experience, rather then improving or changing the existing emotions or feelings of the game which are provoked by its base elements and remain the same regardless of what else is added to the experience through their interrelation.
For example: The feeling of awe at a boss might be added through the aesthetic, BUT, the base "fun factor" or "excitement" of the boss remains constant (regardless of whether the music is muted or the cut scenes skipped) and can only be increased or decreased through the DESIGN of the gameplay.
This is my belief.