No.  It's not true.  He was a good friend of Rand's, and some would say a follower, but they never quite agreed on philosophy.  I think he was a member of the Collective, though -- by the way, the most ironic name for such a group of people that could've possibly been thought of.  Greenspan has always been a believer in the activist Fed, which is, of course, the opposite of the Randian and Rothbardian views that hold it to be totalitarian in nature.

Be nice to America. Or we'll bring democracy to your country.