I'm sure it doesn't charge and that would be rather pointless anyway... Since I got my first B&O remote in 2007, I haven't yet replaced a single battery (I use exclusively Energizer Lithiums). If you put in rechargeable batteries, they self-discharge faster than that even if you don't use the remote at all!
Also, I can't see how you could use the remote on that stand without it tipping over, and if you have to pick it up anyway, why not just keep it flat on the table. Perhaps it's useful with a BL5000 in a 2-way environment.
So in a word, seems like a rather pointless gadget to me, but I have to admit it looks nice