Theoretically it could but it is unlikely unless the child has been in contact with a rabid animal, develops it then bites another kid. But that doesn't mean human bites aren't dangerous even if rabies is less likely. Other illness can be transmitted like hepatitis, HIV, and a variety of other things. This is why most preschools and elementary schools require children to get vaccinations. Though the illnesses can be spread by other means than bites. The only way to be sure is to get your child's blood tested for anything common to your area or simply ask what the other kid has been immunized or treated for.