Most if not all the LEDs I've charlieplexed were common cathode, not common anode, and I'm unsure if it works the same with common anode, but it seems like it should.
Of course it does. In fact, it generally works better
because you will use NPN transistors as the emitter-follower buffers to drive the high side to multiplex, so you are driving all colours of each LED at a time.
Now (as a separate point,) someone happened to mention PNP drivers for conventional multiplexing (as common-emitter). There is an interesting reason for using NPN high-side buffer transistors for Charlieplexing since you are using a negative ground supply system. By using NPN emitter followers, you connect the collectors to the unregulated
(or a least, higher) supply so that the actual current the LED array uses is not drawn from your regulator. You still of course, lose 0.7V in the Vbe
drop in the transistor.
The general rule regarding multiplexing or
Charlieplexing, is that you really do not want to use more than an 8-way multiplex to maintain overall brightness.