2 (maybe 3) problems I can see:
1) The point Juan makes
2) Where would the user store the address for the moodle they want to access? I doubt google would add an extra profile field unless there was something (eventually financial) in it for them...
3) What else would your app offer? Surely it's better that anyone who can code contribute towards the official app (that Juan is lead developer for), particularly in terms of making it better at handling quizzes and other core or guest activities (if/when the plugin system that's been proposed is done).