[Coda]

If the outsider is at rest relative to the moving platform, and the moving platform is in fact accelerating upward, then yes, in the end, the ball does accelerate upward in the end. The observer will see the ball accelerate downward until it collides with the platform, then accelerate upward as the platform pushes it back up.

You can determine the position of the ball at any point in time if you know where it started, where the platform started, and the acceleration of the platform.

The more interesting question is if the platform is accelerating DOWNWARD independent of gravity, because then the ground is falling away from the ball at a different rate than the ball is itself falling.