No, because the Soviets have to in on faking the moon landing. They were also landing a spacecraft at the same time as the landings. To fake the moon landing you'd also have to fake the entire cold war.
Both sides get a great boogie man to denounce. Save a bunch of money on arms if they're mostly fake. Once you learn about the Van Allen Belt, you call over on the red phone and say hey guys, we know we can't send people, but think about the ratings? Maybe we send you a case of Pepsi and we're good?