As far the correlation in general, as I mention in the thread above, these aren't normal people, they're the leaders/overseers of the company using (or not) a landmark initiative whose leader (Vic Gundotra) clearly thinks that ideally it'd be used for both private and public interactions. At the very least, it'd look a lot better if they had accounts, tried making a public post (even just to congratulate the team publicly), and looked a bit more publicly engaged.
However, you didn't entitle your article, "Google Management Doesn't Care About Google+" You said, "Google Management Doesn't Use Google+". The former expresses your perception of Google strategy backed by the data you've collected. The latter is merely link bait.
I do congratulate you. The link bait worked.
"Further, I think it’s reasonable to assume a correlation between private use & public use: if you were constantly posting things on a service and each time you were given the option to make it public or private, surely sometimes you’d make it public, especially as a somewhat public figure wanting to help your own company’s new service get going."
This is fallacy, and it is not even persuasive fallacy.
I make significantly more private posts than I do public posts. I've made exactly two public posts since using it in the early field testing days, and have many more private posts. The friends in my circle tends to share privately, not publicly. You don't have to make public posts to use Google+.
We can say for certain that Google management do not make public posts. We cannot say for certain that Google management do not use Google+ at all.