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?
Sorry, there's currently no VPN/private IP support for Cloud SQL. At the moment, you can use instance settings to control which IPs are allowed to connect. By default, the mysql server is locked down from all external connectivity.
Connecting through a VPN should not improve latency and may in fact hurt it depending on how things are setup. I would recommend doing your own test if that's something you wish to verify.
You can also use the Cloud SQL Proxy to connect externally which uses SSL certs to establish an SSL tunnel to MySQL.