Yes, they would still be balanced because their masses would not change.
On the Moon, the force of gravity is weaker than on Earth, so their weights would change. However, since weight is dependent on both mass and gravity (weight = mass x gravity), the ratio of forces acting on the seesaw due to the masses of the children remains the same regardless of the location. Therefore, as long as their masses remain unchanged, they will still balance on the seesaw.