Correct x 2
The key point is no energy was lost or gained while rolling around the geodesic and the balls energy is unchanging. So constant motion or stationary objects can both have a constant amount of energy. We could take the idea further and spin the ball and now roll it around the earth and now it has even more complex motions yet the energy remains constant.
So constant energy does not require simple straight line motion or no motion it can occur in the most complex movements.
Nothing changes in relativity with spacetime your ball is still rolling along a geodesic which has the same relative time and so no energy is lost or changed. However rather than need a force of gravity to hold the ball against earth like classic physics the ball is trying to run down the energy gradiant provided by the change in time towards the centre of earth and it is that energy gradient that holds it against the earth. The two situations are indistinguishable under classical physics tests you are simply replacing a force with an energy gradient.
You obviously need to do different tests like to see if time changes in the presence of a gravitational source.
