I don't recall ever seeing a DVI connector for the gamecube, so you're SOL there. However, if you haven't purchased the cinema display and are just shopping for one .... get the Dell 24" instead. Those have DVI, VGA, composite, and S-video inputs. So attaching consoles is a breeze.
Yes, no. That is, Angrist is correct. All current-model Apple displays have DVI-input only, and even the early Gamecubes that could output a progressive signal could only do so via component cables (same with the Wii--component only, no HDMI or DVI).
As said, there are large monitors from other makers that can take "TV" style inputs, though, Dell among them.