Not any more than the GameCube does, and actually a little less than the PS3 will (in a way).
Both the GameCube and Xbox 360 use chips derived from PPCs. The GameCube uses a G3 derivitive, and the XBox 360 uses a G5 derivitive. But they are still very different from the processors used in Macs.
The PS3 also uses a PPC-based core. But the PS3's processing architecture is very different from anything else; it uses one central core (which is very similar to the G5s Apple uses), and a bunch of small SPEs (synergistic processing elements) that do most of the big number crunching.
Anyway.....
I'm not impressed with the XBox 360 at all. I'm not particularly impressed with the PS3 either, but it looks better, at least. Personally, I'm most excited about the Nintendo Revolution (which I think also uses a PPC derivitive, by the way). Sony and Microsoft have no vision; their consoles are simply evolutionary advancements over the previous generation. Which is fine, don't get me wrong, but the Revolution looks like it'll be all that and more, based on what we know of its 3D motion-sensing controller.
Unless MS gets wrestles some major third-party support away from Sony, I will not be buying an XBox 360.