As the other poster mentioned, it could disturb the yeast cake and effect flocculation. It might also be possible to jostle some of your airlock liquid into the fermenter.
I really can't image the bouncing around to be a huge concern. I'd probably stick a few towels or a mat under the carboy and call it a day. Having the ideal fermentation is more important. You probably know this, but keep in mind, the temperature of concern is the temperature or your beer, not the ambient room temperature. Using a swamp cooler to maintain a stable temperature might also decrease the vibrations to your carboy in your case.