Course they do for hacked accounts and what not. They keep logs on everything they even send reports on your PC and what not. I called up support once about a bug and they knew the spec of my PC and I never told them. "we are sorry its a bug with the patch for the X2 processors"
They can EASILY be found by getting a job at Blizzard and working in the World of Warcraft Section as a GM.
Like they would give that information to anyone that asked. They could get sued for invasion of privacy.