Can pet cats sneak in and harm my baby while he's sleeping in his crib?

Not really: Kids and pets have coexisted as long as we can remember. Cats are no exception. You might want to place some of the infants clothing where the cat can smell them and do not forget to spend time with the cat while you are with your baby. As with any animal, any pet will become startled with abrupt movements, and might scratch or bite. But no, they will not deliberately go in the crib to harm.

I would encourage : You not to house the cat and baby together in the same room. Many sites document that an animals behavior with an infant can be unpredictable when the adult human is not present.

Mostly myth: Years ago a cat sneaking and "stealing the babies breath" was offered as a reason for crib death. It is mostly myth, but cats and other animals and small infants do not mix well.