Yes that info would certainly help a lot. But the first thing that comes to mind is google TOS. It would also raise a lot of red flags with users that could do more harm than good. It would also be really easy for guys like Brad Geng to tweak the code to do something malicious.
With that in mind, I'd recommend treading carefully. Require users to volunteer the info, even if you only collect a tiny fraction of data. Maybe push the data using HTTP GET or something that's really obvious. And rather than silently sending the data, just pop up a browser with the address pre-populated, so all they have to do is click OK in their browser. Or make the page a form whose fields are pre-populated by the app.
On the nuts and bolts side, I would suggest collecting the GL renderer string in-game but persisting it to the AppData class or something. Then the data could be sent at any time (or sent with crash reports in the custom entries), so as not to interrupt game play. You could start by just making a top-level menuitem to send the data, and if the data is a trickle you could step it up by adding a nag dialog or something on the next release.
On the server side, a few thoughts. Might be easy to use google docs/forms for the backend. Or maybe your forum here has a way to catch data. Could be something custom, or if the forum supports polls you might be able to bend that to your will. Another option might be the new Google Play Game Services. You could create achievements or something to motivate voluntary submissions, and/or use it to do the actual data collection. Like a nugget is stored in the user profile or something.
Back to google TOS, another thought would be to put the data collection thing only in the apk version posted here on the forum.
