I run AACW demo on the following system:
IBM Thinkpad T40 laptop
Intelx86 1300 Mhz
256 MB RAM
32 MB 7200 Mobility Radeon
Omega drivers
Virtual memory set to 1792 MB
No crashes so far. Scrolling the big map can be pain, but you can get to different, distant locations fast pinpointing them on the minimap rather then slowly scrolling the big map. Memory leak after 5-6 turns with AI/extra time option on.( I use AI all behaviours/small FOW bounes/no extra time for enhanced AI performance, then the game runs ok). I have had NO graphics problems so far.
I thought I wouldn't be able to play the demo due to the outdated graphics card, but I am playing it.