I've never had the occasion to chase one while in motion, although I've found them way out of place and - sometimes - tipped over. I won't bother you with those stories.
As for chasing 'em, ask Monte Warnock. He seems to have the best stories about moving toilets, such as seeing a handicap unit (much bigger cross section), door wide open (bigger still), sitting on the water on the surface during a storm. The water made the surface really slick, and with the door open -- Monte said he chased it in his truck and the toilet was moving about 7 mph. As for having one of them go through the traps - well, i take those stories with a grain of salt, because by the time the weather is bad enough to send toilets flying - the timing light equipment is shut down. Makes for a good story, though.