I've seen it done all the time, it is quite relaxed and natural. Have you watched latin dancers in latino clubs? Put someone doing ballroom hip motions in the crowd and you can pick it out in a heart beat.
How is it possible to move your hips without shifting your weight? Even if it's just shifting your weight to a different part of the foot instead of from one foot to the other, you can't move your hips around without changing your weight placement. It's just not physically possible.