No - the ball is not defined as part of the hands. And the hands are not part of the bat. (
) This sort of invention of definitions is just the kind of thing that will make a young official misrule on something.
The ball is the BALL. Period. The rules do not say that the ball-carrier is down when the ball hits the ground in his possession... therefore, he is not down. The ballcarrier is down when any part of his BODY other than hands or feet, touch the ground. Did any part of his body touch the ground? No. Play on.