How to get Geocoding to use my Google API key?
You weren't imagining things. CiviCRM 4.6 and 4.7 until recently was ignoring the Google API key altogether! I'm not sure the history of that, but it would have been great if someone had documented that in the settings. As of the latest 4.6 and 4.7 the Google API key is getting recognized again (https://github.com/civicrm/civicrm-core/blob/4.6.23/CRM/Utils/Geocode/Google.php). Once I upgraded, I checked the URL getting passed and it now attaches the key and uses https (the other requirement of Google). And in the API dashboard I'm now seeing activity.

So the answer to your question is: upgrade CiviCRM to the latest in order to get Geocoding to use your Google API key.