No. Not much. He would, though, remember certain things that Omega remembered. Most importantly, he would remember Tex-- no, Erastis. Or, what Erastis had been based off of. The dead wife of the Director. Alpha had been created from a living man, based off of a living brain, and there had been plenty of him to go around. They had been able to force him to split and use those pieces. But Tex? She had been created years after the Director's wife had died, and she had been created from memories about her, and nothing more. She was a smaller program, but more advanced, made years after Church. Made for Church.
He'd remember (his own memories from when he was a young Spartan, around twelve.. his first real memories, not installed ones) Tex being favored by the Director, who would later induct her into the Freelancer program. How he'd doted on her, how he'd treated her differently than the others, how he'd looked at her.. and Church would understand that now. The Director had been in love with his own program. Then he would remember being split apart-- splitting himself apart, in fact. But not why. Not the torture. But he would remember losing pieces of himself, feeling incomplete. Church wasn't real. And it was obvious by the way that Tex was staring at the ground, that she understood she wasn't real, either.