Have you tried downloading your data from Google? If you have a large data set (for being a loyal user for years) and a slow (non-business-class) internet connection, the server just expires your auth token before you can complete the download.
The question is if they have to give you your emails if they still have them. I think it would be decided they would have to. It might be worth getting ready to be blocked, get blocked, and then demand the data to set the precedent actually. But I am lazy; the virtue of a programmer, the vice of a concerned citizenry.