CD players 20 years ago were usually audibly transparent. The tech has improved (cheaper, smaller, better numbers), yes. But if they were already audibly transparent 20 years ago, then all they are now is even more audibly transparent. In other words, they sound the same.
Yes, it's possible for different CD players to have audible signatures. But why would they do that? Doing so would mean purposefully messing up the design and altering the frequency response away from flat, or adding noise/distortion when it is unwanted. Any competent designer avoids those mistakes.
Now, on the other hand, the marketing team will take those designs and come up with all sorts of colorful prose telling customers why the more expensive players are better.
What is audibly transparent and how do you define it? What kind of measurements will differentiate between an audibly transparent and one that is not?