Originally posted by Just4Hax
Yes. First your consciousness falls into the dream state and then your body.
Actually, I thought it was more of a gradual process, with the brain going through certain "states" (theta, gamma, beta, etc, I'm not sure which ones apply to sleep though). Because there're multiple levels of sleep, too, like R.E.M. and the level you enter when your mind is preparing to awaken.
Also, some people can train their bodies to go into their sleep state before their minds, giving themselves "sleep paralysis." It's supposedly a way to easily enter a lucid dream.