Much like the "Native" AWS RDS Integration with MySQL, you can set up a Datadog Agent's MySQL integration to monitor on a MySQL instance running in Google CloudSQL. With this setup, you can complement the metrics you would otherwise get from Datadog's Google CloudSQL Integration with the metrics available from the Datadog Agent's MySQL integration.
To set up this "extra" integration on your Google CloudSQL instance, you can set up the MySQL integration on a Datadog Agent and configure it to remotely connect to your Google CloudSQL instance instead of using the localhost default. The setup steps are otherwise the same as any other locally hosted MySQL instance.
With one caveat: Google CloudSQL does not support performance_schemas, so you can't
GRANT SELECT ON performance_schema.* to the datadog agent user. As a result, two of the MySQL check's extra/optional metrics (listed here) will not be available for Google CloudSQL instances. Otherwise, the integration should work just as it would with any locally hosted MySQL instance.