Answer
No, in the classical picture.
Work Step by Step
For a planet circling the sun, it has so much angular momentum that its analysis falls squarely in the realm of classical physics. That is, any quantization of the angular momentum may be ignored.
This is similar to saying that the amount of water we can pour out of a glass is continuous, even though technically, it is quantized on a molecular level. Our assumption is justified because the amounts of water we deal with are so much larger than the “quantum” of water that we can neglect the fact that water is quantized.
