CiviDesk's Google Apps Sync Extension
I haven't heard back from CiviDesk, but I did go on github and find version 1.1 which claims compatibility with CiviCRM 4.5. I felt like that was close enough to my 4.7.3 for me to take the leap. I initially got a bunch of errors (see list below the break), but they are not persistent.

My Results

Success. The only errors I've spotted were due to my contacts data having undesirable unicode characters. Once corrected (By editing the table civicdesk_sync_googleaps) the next cron run or forced execution puts it back to work. 

What to expect in your Google Apps Directory when the sync happens:


Wait 24-48 hours for the first results to appear. You can blame Google for that.
Pre-existing contacts are not updated or deleted. New contacts will be ADDED to the Google Apps Directory. On subsequent runs, these newly-added contacts should update as CiviCRM does (I base this on the fact that the extension records Google's own contact ID for what I can only assume will be future use).
Added contacts will be populated with Name, Organization, Job Title, Email, and a link to their CiviCRM profile. As far as I can tell, mailing addresses are NOT synced.
The default sync speed it 50 contacts per cron run. I cranked mine up to 100 with no ill effects.


That's about it. I'm including error messages below for searchability reasons for the community--I'm not expecting anyone to offer fixes especially since they were just one-time errors.

-- Just error messages below. Avoid reading further if they make you sleepy. --

Notice: Undefined index: child in _cividesk_insert_navigationMenu() (line 58 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/cividesk.ext.php).

Notice: Undefined index: oauth_email in CRM_Admin_Form_Setting_GoogleApps->_checkOAuth() (line 142 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: oauth_key in CRM_Admin_Form_Setting_GoogleApps->_checkOAuth() (line 142 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: oauth_secret in CRM_Admin_Form_Setting_GoogleApps->_checkOAuth() (line 142 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: domain in CRM_Admin_Form_Setting_GoogleApps->_checkOAuth() (line 144 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: domain in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 44 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: oauth_key in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 58 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: oauth_secret in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 63 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: last_sync in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 74 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: processed in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 75 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).

Notice: Undefined index: oauth_email in CRM_Admin_Form_Setting_GoogleApps->_checkOAuth() (line 142 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: oauth_key in CRM_Admin_Form_Setting_GoogleApps->_checkOAuth() (line 142 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: oauth_secret in CRM_Admin_Form_Setting_GoogleApps->_checkOAuth() (line 142 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: domain in CRM_Admin_Form_Setting_GoogleApps->_checkOAuth() (line 144 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: domain in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 44 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: oauth_key in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 58 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: oauth_secret in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 63 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: processed in CRM_Admin_Form_Setting_GoogleApps->buildQuickForm() (line 75 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined variable: resetStr in CRM_Admin_Form_Setting_GoogleApps->postProcess() (line 124 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/CRM/Admin/Form/Setting/GoogleApps.php).
Notice: Undefined index: processed in civicrm_api3_job_googleapps_sync() (line 184 of /home/mysite/public_html/sites/default/files/civicrm/upload/com.cividesk.sync.googleapps-1.0/api/v3/Job/GoogleappsSync.php).