Google would want to use information that would be relatively uniform over its entire index. Clearly, not everyone has Google Analytics installed, nor are the installations uniform, so that in itself would make it a bad choice to use.
I doubt that they use it even for manual audits, but I'm sure they're in some way looking for big data correlations on the installed base that might help them confirm patterns they're seeing in other ways.
Perhaps they check aggregate correlations on types of sites to suggest ways of improving both Analytics and the algo. Too "noisy", though, and too invasive, as a ranking metric.