I'm not sure he would have had much time to know. Even if he was an active member of the KGB with a professional handler, he was arrested within a few hours. He attempted to die in a shootout with the police (which no one brings up regarding Jack Ruby killing him, when he tried to kill himself), that's why he was stuck in a jail.

As a result, if the Soviets sent him, and didn't want anything to do with it, they'd be in a panic to burn everything related to it, and shoot everyone involved in it.

Which is interesting because the records weren't destroyed, and the recruiters and handlers weren't executed.

And as for Posadism, yeah, it's pretty bad. I think Kruschev understood that he could never actually win a nuclear exchange, especially given the industrial difference. The entire Bomber Gap scandal demonstrated that the Americans could mistakenly build 2,000 nuclear bombers because they thought the Soviets had more, not realizing the Soviets only had 12. The nuclear sub program was basically the only hope that the Soviets would have to retaliate if the Americans launched first. They were never going to win, but too many Communists didn't get it. I have an atlas that actually contains a map of the Soviet plan to invade Europe in 1990 that was developed because they were concerned Reagan would attack.

There is no record, that I have seen, of an anti-war or anti-nuclear program in the Soviet sphere of influence. The ones in the west were all nearly explicitly funded by Russia.