The Soviets know a thing or two about lying. The instant anybody finds a flaw in this Moonshot stunt, they will become the laughingstock of the world, and the world is full of people who would want to find a flaw. The best kept lie is nothing less than the truth. If they manage to develop the necessary technologies to nearly land on the Moon, then they're going to go the rest of the way. Even if the Cosmonaut puts his pinkie toe on the surface and picks up a pebble, it would still be impossible to debunk.
If they do try to do this fake, or if they actually do a Moonshot like I suggest they would, then there are still repercussions in the Soviet space program. They're doing to need to launch an N-1 sized rocket to the Moon, America would be watching the launch and observatories and tracking stations throughout the First World will be following its path. The N-1 will have to actually work. Even if they don't land on the Moon, that is a powerful tool for the Soviet space program to have. Salyut would be the same size as Skylab. Soviet interplanetary probes could afford to be much bigger and more capable. At the very least manned circumlunar flights with the Soyuz would be possible. And as a knock-on effect, the Saturn V is unlikely to be removed from production, as Congress probably doesn't want Ivan to have the biggest rocket around.