No, it only supplies the CD player (I mean, it COULD supply the pre-amp, if the pre-amp were compatible) (which mine isn't).
I think the point is that separating out the power supply enables it to be bigger, of a higher quality, and more isolated. Which impacts sound.
But that's not the real point. The manufacturer's intent here is to provide an easy upgrade path. You can buy a very good product at a certain price point, and then a few years later make it better with an additional cash outlay (an amount you might not have wanted to spend when you bought the product at the outset).
Let me put it this way: a couple of years after I got my last CD player, the manufacturer offered an internal power supply upgrade. Before pulling the trigger on the upgrade, I auditioned modified v. unmodified versions of the CD player at a store. The difference was NOT subtle. So, yes, with CD players the power supply somehow matters.
These guys just make that kind of upgrade easier: instead of having to ship my CD player back to them and then wait a few weeks while they replace the power supply (as I did when I upgraded my last CD player), I simply buy the external supply and hook it up.
So I think the point here is that the external power supply is higher-quality than the built-in one, not that it's external. (Although I'm sure that isolating the power supply does provide additional benefits.)