Your question is at risk of over-simplification of the fall of the USSR and other Communist countries. If you want to pin point one thing, you won't be able to, but at best you'll want to widen it to perhaps western influence or the inflexibility of Communism, but no, IMO, Radio Free Europe didn't have a major impact in "defeating communism", which is also a problematic statement, because Communism is still around. ANYWAY. To get back to your question, and sorry about the sidetrack there, it was a mixed audience in Communist countries. Sometimes people preferred to listen to RFE, and some people thought it was bogus. Think about it like the Daily Show here, some people think it's just propaganda from the "Liberal Media", and for some people that's their only news source. Typically, though, if you were a high-ranking communist, you wouldn't admit to listening to RFE, but if you did, you had to espouse your dislike for "Capitalist propaganda".

Anyway, I hope this helped. I'm reading Kovaly's Under a Cruel Star, where they talk about listening to RFE a lot.