The propbability is nonzero by QM, but is so small that it would take probably many and many times the age of the universe to become a reasonable chance to make such a leap (even a mm probably).
It is actually quite different, maybe not in principle but at least to many degrees of accuracy. For the many particles of which the moon consists, the quantum behaviuor can be safely neglected and we can speak of it's position and followed path and orbit.
In principle still nonzero, only unimaginably small.
If you (by followoing this persons argument) you would consider the moon as one entity with a single wavefunction (which is quite reasonable) with this wavefunction a huge mass is associated. By Heisenbergs uncertainty principle there is a very small uncertainty in the the verlocity and position of the moon. In a formula
[tex]\Delta x \Delta v < \hbar/2m [/tex]
So the product of uncertainties in velocity and position of the moon is smaller than the unimaginably small number on the right. For all purposes the unvcertainty in position (and thus the chance of the moon leaping to some different position) is negligible.