I think they did even though the Soviet Space Program was a lot better then NASA at the time, and the soviets were the first to send a human to Space. How many times have humans gone to space since 1969?
What a sorry state NASA is in today though

Needing to pay the Russians to send U.S Astronauts to space as they are shutting down manned missions due to Budget and safety concerns. This wouldn't have occurred in the Cold war
