Yes, Schrodinger’s equation would be valid when applied to the solar system. However, the results it gives would be identical to those of classical physics, at much greater computational cost and complexity, so it would not be at all useful.
Work Step by Step
If a new theory is valid, it must give the same correct results as the old theory, i.e., it must correspond, in any area where the old theory has been verified. This is discussed on page 611.