Yes, I can understand the thought process behind Ivan’s assertion, but don’t agree with it. As far as I can understand, his assertion probably arises from an inability to reconcile his difficulty to believe absolutely in the existence of the divine when considered against sufferings, cruelty, etc prevalent in the world. This type of existential uncertainty can lead to certain degree of maybe fear and frustration that can lead to such kind of nihilistic outlook. Anyway, this is how it seems to me.
Now I do not have much knowledge of Christianity, but as you said, I did feel that this work advocates for Christianity. Especially if we consider this quote: “What matter that he now rebels everywhere against our power, and takes pride in this rebellion? The pride of a child and a schoolboy! They are little children, who rebel in class and drive out the teacher. But there will also come an end to the children’s delight, and it will cost them dearly. They will tear down the temples and drench the earth with blood. But finally the foolish children will understand that although they are rebels, they are feeble rebels, who cannot endure their own rebellion. Pouring out their foolish tears, they will finally acknowledge that he who created them rebels no doubt intended to laugh at them.” Even though these are just Ivan’s words, it does feel that even the author probably feels similarly. These words also bring out the degree of conflict Ivan’s in.