God cannot be called infinite goodness and there be evil in the world unless the evil he allows would lead to good. In fact, this even is not enough, for God cannot be called infinite goodness and there be evil in the world unless the evil he allows would lead to a greater good, a greater good that is so good that the allowance of evil would be desirable to begin with.
It must be that allowing evil is better than the mere absence of that evil to begin with, for evil exists. We see that an even better outcome is necessitated than there being no evil in any case, the outcome being that the presence of evil leads to greater good than the good of there being no evil to begin with.
For if it were merely that evil brings about a good, it is a cruel game, making evil unnecessary. But if evil were allowed to bring about an even greater good, so great, that it would make the allowance of evil permitted or even desirable, as God desired it, for it is present, then yes, this line of thinking is sufficient.