The only tubes in CDPs that I'm aware of are in the analog/output stages of the players. In the early days of CD, the use of a tubed output stage often had the nice effect of taming some of the digital "glare" exhibited by the early players and CDs--my Analogic Designs (Scott Nixon's original company) CD player may not have had the hyper detail of the Magnavox 472 on which it was based, but it was FAR more listenable and enjoyable for music. As digital and CD players have evolved, the use of tubes in an output stage doesn't necessarily "soften" the sound (although it certainly can, depending on the design and tubes used), but on well-designed units has a three-dimensional palpability to the soundstage images that most solid-state dsigns still don't quite match, in my view. They may not quite have the control in the deep bass of solid state units, but they have good quality in their bass reproduction, and depending on the tubes used might have a lusher midrange. These are generalizations, though, and not true in all cases. You do need to let the tubes stabilize before listening to music, but it doesn't take that long, and there is a period as they warm up that the sound will continue to improve. I tend to leave my tubed DAC on for long periods, because it usually takes a half-hour or hour for it to sound its best, as with most tubed equipment I own.
If there's any way you can listen to a Shanling CD player, either at a dealer or through a friend, it would be instructive because, at least in its original version, it had both solid state and tube analog stages, each with its own set of outputs, so you could hear the difference between the two quite easily. When I heard it at my dealer's, there were some discs where I preferred the tubed output, some with the solid state output, but overall the solid state output seemed a bit cleaner. Who knows what would happen if you changed the tubes, though...