Yes, they would still be balanced because their masses would not change.
In physics, mass is a measure of the amount of matter in an object and does not change regardless of location (Earth, Moon, etc.). However, weight, which is the force due to gravity acting on that mass, would change because the gravitational force on the Moon is about 1/6th that of Earth. But since the seesaw balances based on mass (and distance from the fulcrum), the children would still balance if their masses were the same, regardless of their weight being different on the Moon.