Draft Deployment: Remove "Okay. Let's get the test version of X"

No. The question comes up fairly frequently on the Google+ support page but essentially it boils down to this - there are test apps and public published apps. If you want to make an app and deploy privately your only option is to use authentication.

That said, if you give your Action a name then you can invoke it by speaking its name into the microphone on a device (phone, Home etc) or the simulator. That will remove the annoying "my test app" bit, but you'll still hear "the test version" quip before activation.

Finally, you can allow others to use the app if you mark them as "testers" in the Actions console.