The question is not absurd. Our conventional view of happiness is as an emotional state of mind. But is God subject to emotion? Certainly, we are told that God loves His creatures, and love, at least in the human world, is an emotion. But love is a source of happiness when it is reciprocated, and God’s love is reciprocated only by some of His subjects, by no means all: some do not believe that He exists, some do not care whether He exists or not, and others hate Him, accusing Him of indifference in the face of human pain and misery. If He is not indifferent, but subject to emotion like us, He must live in a constant state of sorrow when He witnesses human suffering. He did not cause it or want it, but He is helpless in the face of all the misery, the horrors and atrocities that nature brings down on people or people inflict on each other.
If, on the other hand, He is perfectly immutable, He cannot be perturbed by our misery; He must therefore be indifferent. But if He is indifferent, how can He be a loving father? And if He is not immutable, then He takes part in our suffering, and feels sorrow. In either case, God is not happy in any sense we can understand.
We are forced to admit that we cannot understand the divine being—omnipotent, omniscient, knowing everything in Himself and through Himself, not as something external to Him, and unaffected by pain and evil.
The true God of the Christians, Jesus Christ, was not happy in any recognizable sense. He was embodied and suffered pain, he shared the suffering of his fellow men, and he died on the cross.
In short, the word “happiness” does not seem applicable to divine life. But nor is it applicable to human beings. This is not just because we experience suffering. It is also because, even if we are not suffering at a given moment, even if we are able to experience physical and spiritual pleasure and moments beyond time, in the “eternal present” of love, we can never forget the existence of evil and the misery of the human condition.