Toy with non-waterproof battery box: is this an issue? What will happen?
If I understand this right, you've got a electronic product that is intended to be used immersed in water, but it leaks and water can get onto the electronics.  Seriously!!!?

In case you really are serious, yes, that is a problem.  Even if the water only gets to the batteries, it can cause corrosion and will provide at least some leakage path for battery current, which will discharge the batteries prematurely.  Pure water has pretty high resistivity, but it doesn't sound like you get to control the cleanliness of the water.  Even a little salt, for example, will greatly increase conductivity.

There is little danger from the electric current since it will be largely inside the battery box, but again, seriously!?  You are really thinking this might be OK somehow?