I\'m testing with Google Cloud Endpoints on App Engine and I\'ve mapped my app to a custom domain. It appears that this is not possible. I\'ve tried accessing the endpoint url,
Correct, you can not map to a custom domain at current.
edit: Google CloudEndpoints 2.0 will support this, which is now BETA. As explained by Google in the link below.
Google has now announced this "will be supported" but has not given an ETA.
https://code.google.com/p/googleappengine/issues/detail?id=9384#c44