AC can perform electrolysis although the reaction intensity is diminished because of the nature of sinusoidal power signals canceling out at certain time intervals. DC performs electrolysis much better than AC, although pulsed DC is also utilized (absolute value of a square wave). AC is typically used in situations where high power is required, more-so than can be supplied by batteries; modification of the sinusoidal signal is typical.

Ehhh, I'll let the article sit for a while to think about the best way of saying things. Your right that DC (battery) is the most common power source for standard demonstrations.