Oh of course, but I wonder if by the time you'd created that system, you'd feel the result was worth it? Is what Echo offers really so valuable you'd go through the trouble? I wouldn't.
I don't own an Echo because I don't feel the convenience of such a device is outweighed by the obvious privacy implications. I would be more likely to use it if it was located within my home but at that point the limiting factor would probably be cost. This is why such a device would have to provide additional functionality.
In a world where it is just expected that you have a personal cloud server in your home Alexa becomes an "app" on that server and the Echo continues life as a very nice speaker/microphone device you can place in a visible area in order to interact with that server.
