Well, her circle was pretty influential, so I think it's interesting from a sociological and political perspective. I'm not that interested in the who-Rand-slept-with aspects, but things like "Rand had a close inner circle that Alan Greenspan was once part of" are interesting/useful to know.
That is somewhat interesting in terms of the intellectual history...
Nathanial Brandon: his writings most resemble modern psychology, and Rand was opposed to making her ideas sound like psychobabble... hence her use of "selfishness" rather than the looser (though more descriptive) "self-actualization".
Greenspan: One simply cannot thrive in politics by discussing the morality of capitalism (other than by criticizing it). Greenspan omitted any mention of Rand from his most recent book, and all we have is an essay he wrote. Meanwhile he officially ate crow after the financial meltdown by making some remarks critical of capitalism.
It would indeed be interesting to listen to tapes of their debates, but short of that I think it would be fairly difficult to learn much, since Greenspan himself is mum.