Hi Mike
Sadly it is not possible to use the authentication that is stored in the local file outside of the Google Authentication node. You could use it when you use the Java snippet node and Google libraries, but that might be out of scope.
The workflow that you attached however should provide you with the necessary access/refresh token to issue your queries. I guess you found it here. If you follow the step by step guide you should end up with valid tokens which you can use in node #167 (Create Request With Access Token):
The following GET Request node should retrieve whatever your request is.
In step 2. you need to activate the appropriate API for your call, in your case I guess this would be the Google Analytics API.
Maybe this helps Otherwise, to help you further, it would be interesting to know what problem you are running into with the workflow.