You can get the android google account from a device using the AccountManager like this:
Account[] accounts = AccountManager.get(this).getAccounts();
for (Account account : accounts) {
// TODO: Check possibleEmail against an email regex or treat
// account.name as an email address only for certain account.type values.
String possibleEmail = account.name;
...
}
source: http://stackoverflow.com/questions/2112965/how-to-get-the-android-devices-primary-e-mail-address
You might want to check on account.type to match “com.google” since many other synchronisation accounts exists on a regular device. Think of facebook and weather synchronisation.
Also this requires the GET_ACCOUNTS permission set to your manifest: