I need to define the root password of my Google Cloud SQL instance to be able to connect using MySQL Workbench. Will defining the password interfere with the connection to the database of my AppEngine application? Or an application running from AppEngine have a different access than external tools?
The problem here is that the service must be always available and I am afraid of dropping my service for some time, while doing a deploy with the new Cloud SQL definitions, after changing the password.
If you are talking about setting the root password using the Cloud SQL UI or gcloud command, it won't interfere.
That operation sets the password for root@% which includes every host except locahost. AppEngine uses the root@localhost user to connect to your Cloud SQL instance.