I am developing an Android app that uses Google Cloud Endpoints on Google App Engine (in Python) for its backend. The Android app authorizes the user using Google Play Services
In the local environment, the dev_appserver is the API server. If you've configured it so that it's accessible from machines other than localhost (i.e. another machine/device on the network) API requests should be accessible as well.
However, there's currently an issue with the local server and gzipped requests. Until that's fixed you'll need to disable gzipping within the client library in your Android app (see this post).