Can you jump start a car that its battery is wet?

Yes. The 12 volts of a vehicle battery is not sufficient to shock you nor is there enough potential to be significantly affected by the electrical resistance caused by the water. The low voltage of the battery and the jumper cables will not harm you.

Just don't touch the spark plug wires or the distributor while the engine is running or you're trying to start it; THAT voltage is high enough to give a thrill you won't soon forget.