As an aside, the doctor was asking about where they could have picked it up. I mentioned that they had recently started at a new daycare. The doctor immediately remarked that it was probably an un-vaccinated classmate. So, once again, I recommend you vaccinate your hypothetical kid. If not for your own kid, then for everyone else's.
While that sounds pretty good, I'm fairly certain from a logical standpoint the odds of impacting the moon are as good or worse than the odds of leaving orbit and flying out into space. (Especially with the low gravity levels of the moon.)
I'm less than certain. Intersecting with the Moon would only require changes in ellipticity, whereas causing the satellite to become unbound would require a considerable increase in the satellite's kinetic energy.