John Gruber among others note that Google DNS service is not tied to Google Accounts. That’s not just wording in their privacy statement, it’s technically impossible for them to do otherwise, at least with reasonable accuracy.
Your computer is associated with a Google account via a cookie given to you when you login. Cookies are sent back to Google’s servers as HTTP headers whenever you fetch something from the host that set the cookie (every request, even images). They can only be sent to that domain, nobody else.
DNS doesn’t operate over HTTP, and therefore can’t tell what Google Account you’re using.
Google could however use your IP address you used to login to your Google Account and associate it with your DNS activity, but that would make the statisticians at Google cringe. So many homes and businesses have multiple computers behind a NAT router. Google DNS is unable to distinguish between them. Even one computer can have multiple users.
Before someone jumps up and says “MAC address”, the answer is: NO. To keep it simple a MAC address is part of the “Data Link Layer” of the OSI model (Layer 2) and is used to address adjacent devices. Your MAC address is only transmitted until the first hop which would be the first router on your way to Google. Each time your data makes it to the next device on its way to Google the previous MAC header is stripped off and a new one is added. By the time your bits get to Google that packet of data has only the last hop’s MAC address on it. Many people confuse Layers 2 and 3.