The new Google Cloud SQL Engine creates its own VM instance to run a MySQL database, with an exposed public IP address. I was hoping that it would be possible to VPN into the Google Compute Cloud, then connect to the MySQL VM instance internally. Is this possible? The computer I am trying to connect from is a physical machine located outside of the cloud.
If it's not possible, what if I connect via VPN and use the public IP address to connect to the MySQL instance? Would it resolve to the internal network quickly and mimic the behavior of a local connection (no delay)? Or would it have the same performance as connected to the external IP address with no VPN in place?