Easy to test: close your eyes and have someone else turn the display off and on and see if you can guess, significantly over chance, that it is either on or off based on the sound. (Blind test). Or cover/obstruct the display in some way (curtain/cloth/etc.).
I'm pretty sure there's no reason in physics/acoustic science why that would alter the sound in any way in any level of gear. I've never heard anything of the sort at least, and I have heard pieces that cost tens of thousands with displays on or off at friend's homes (based on their own preferences and whether we are listening in low light or not) and I have several pieces myself that cost many thousands (the most I'm willing to spend on any piece of gear besides speakers).
That you perceive more delicacy, ambiance, and less edge with the display off strong suggests that you are just perceiving that (psychosomatic/perceptual bias) when it is on because it is digital and you associate digital with edge and lack of ambiance/delicacy (a coldness or harshness). Also, the ambiance part could be attributed to you focusing less on the display and more on the rest of your surroundings when it is off.
It's akin to lighting candles or starting a fire when listening to music: often the same gear all of the sudden sounds "warmer" to some who are unaware of the perceptual distortion which is caused by environmental factors and not the gear. When people remark on this, and attribute it to the gear "warming up", I say it sounds the same because I am aware of such distortions and thus more immune to them.
The same affect has been demonstrated with tube or solid state gear behind a curtain: tell the listeners it is tube gear when it is really solid state and they will talk about its warmth; tell them it is solid state gear when it is really tube gear and it will sound cold to them. Then remove the curtain, and Oz like, their illusions are shattered!
We humans have many psychological/perceptual distortions and illusions (a key one is agent/agency detection where there is none) that are hard wired in us as part of our evolutionary biology heritage since they served a purpose long ago (and still do to some extent). But they will deceive us, present untrue perceptions of the world, if we are not careful and aware of them.
Oh, and I leave my displays on. :yes:
