I have the X2.5 which is similar to the X1. From my experience, there is very little difference (if at all) between dimming the lights and leaving it on. Perhaps psychologically my eyes get to relax a little more instead of staring straight at a bright florescent display. Without any lighting, it gives me the impression of a slightly quiet and blacker background. However to answer your question the digital circuits are seperated and isolated from the analog supply. The display circuitry would be isolated from injecting any noises back into the pre-amp. Of course like everything else, any energy that is taken is still energy and so I wouldn't be surprised if the sound does improve with it off. The X1 has an even more isolated circuitry on all levels.
Yet it may be better to ask Nelson Pass or any others out there in the Pass forum:
http://www.diyaudio.com/forums/forumdisplay.php?forumid=8
If you noticed a difference, that is a bonus. I don't believe the lighting option is for sonic purposes but just a convenient way like many other designs to give a choice for those who may be distracted by a brighter display or who like to have different display levels. The Noritake display used in all the Pass amps is designed to have brightness control automatically. The Noritake company if I can recall correctly are the inventors of the vacuum flourescent display and basically have many products out there for the PC,gaming, and electronic displays. You can check their site out at : http://noritake-elec.com/
Hope the above helps.
Cheers,
Zen
