These answers are a bit outdated. Google App Engine instances can connect to an external database server as per https://cloud.google.com/appengine/docs/php/using-third-party-databasesservers.
It's worth noting that theThe ability to connect externally requires that the account the App Engine is running under be a "paid account" a/k/a "billing enabled". See
References: https://cloud.google.com/appengine/docs/php/runtime#PHP_Functions_that_requires_billing_enabled
-https://cloud.google.com/appengine/docs/php/using-third-party-databases
-https://cloud.google.com/appengine/docs/php/runtime#PHP_Functions_that_requires_billing_enabled