I would say in other flamewar topics, publishing data has had a net positive effect. For example, having some data on GPL vs BSD license usage has not killed the flame war but it has elevated some of the discussion. Similar for comparing install/download numbers of Vi vs Emacs. It is unlikely to cause anyone to "switch side" but it reduces the anecdotal noise and focus the discussion to either be about the strength and weaknesses of each side or to be about the data collection method.

I personally can't think of a single flamewar topic where data has poured fuel on the flame and made the discussion worse. Could be a failure of imagination of course but past experience has been clearly on the positive. I see however that the work is unlikely to be done by you all if you collectively don't think it is a good idea.