This YouTube video shows Compiz Fusion running on my work computer. It has a fairly decent CPU (P4 3.00GHz), but no "useless" things like sound cards or (more relevant for this issue) graphics card. The only thing it has is an Intel 82865G graphics chip integrated in the motherboard. We are talking about an integrated chip (not dedicated graphics card) released in May 2003.
Judge the performance for yourself (take into account that the actual performance is higher, since the recording program to make the video also uses up some resources):