Nope, they never created any tech demos for Gamecube. Square's relationship with Nintendo was VERY rocky at that time. In fact, the president of Nintendo at that time said he'd never let Square make a game for a Nintendo system again, even if they wanted to. It was obviously a big shock when Final Fantasy: Crystal Chronicles was announced.
Anyway, FF XI is confirmed for X360, and another mystery MMORPG by Square Enix is strongly rumored. Allard all but confirmed that S-E had another X360 game in development.