Did the Kwisatz Haderach want to die?

This is almost a direct quote from the book, Children of Dune in which Leto II's desire for death is described in rather more detail. In short, he's in immense physical and psychic pain, no longer human, incapable of sleep and haunted by the acts of barbarism that he'll be forced to undertake over thousands of years.

“He runs to tire himself,” Ghanima said. “He’s Kralizec embodied. No wind ever ran as he runs. He’s a blur atop the dunes. I’ve seen him. He runs and runs. And when he has exhausted himself at last, he returns and rests his head in my lap. ‘Ask our mother within to find a way for me to die,’ he pleads.”

Farad’n stared at her. In the week since the riot in the plaza, the Keep had moved to strange rhythms, mysterious comings and goings; stories of bitter fighting beyond the Shield Wall came to him through Tyekanik, whose military advice had been asked.
“I don’t understand you,” Farad’n said. “Find a way for him to die?”

“He asked me to prepare you,” Ghanima said. Not for the first time, she was struck by the curious innocence of this Corrino Prince. Was that Jessica’s doing, or something born in him?

“For what?”

“He’s no longer human,” Ghanima said. “Yesterday you asked when he was going to remove the living skin? Never. It’s part of him now and he’s part of it. Leto estimates he has perhaps four thousand years before metamorphosis destroys him.”

Farad’n tried to swallow in a dry throat.
“You see why he runs?” Ghanima asked.
“But if he’ll live so long and be so—”
“Because the memory of being human is so rich in him. Think of all those lives, cousin. No. You can’t imagine what that is because you’ve no experience of it. But I know. I can imagine his pain. He gives more than anyone ever gave before. Our father walked into the desert trying to escape it. Alia became Abomination in fear of it. Our grandmother has only the blurred infancy of this condition, yet must use every Bene Gesserit wile to live with it—which is what Reverend Mother training amounts to anyway. But Leto! He’s all alone, never to be duplicated.”