They did it right under Khrushchev's nose.
http://books.google.co.uk/books?id=ZhgFUyCOhHcC&pg=PA205&lpg...
And I'll bet it made a fun story for the director of the CIA to tell at cocktail parties.
For example had they realized that the LM the Soviets were building was incapable of working, that could impact the program in huge ways including changing how funding for the US program was structured, rule out or confirm a configuration as viable, speed up development in other critical areas etc...
As to the benefits, it seems they're still classified, whatever they are. The document [1] describes, for example, "revelation of the system XXXXXXXXXX that was used here and conceivably for other Soviet space hardware" as a "positive intelligence result" of the operation.
[1] http://www2.gwu.edu/~nsarchiv/NSAEBB/NSAEBB479/docs/EBB-Moon...