Absolutely not. You can use Cloud Datastore, or you can connect to any database that can communicate over sockets or http, including Cloud SQL. Of note is that Datastore has a free tier, Cloud SQL does not, and Socket usage can incur (some) cost when communicating with other databases.

I've seen many Python apps that connect to a free MongoDB instance hosted on Mongolab.

(also worth noting that Node.js support for App Engine is currently in beta.)

(disclaimer: I work for Google on Cloud Platform)