The API does not provide any method to determine a user's email address and it is unlikely to do so in the future.
This would be a risk to both the user's privacy and his/her trust in Stack Exchange. And, a pressing need for this information has yet to be demonstrated, regarding the API.
Note that Stack Exchange refuses to even provide the user's email hash ...
There is no app, exactly like that but two are pretty close (they don't have any annoying sounds).
These both run on Windows + Linux platforms and provide desktop alerts for favorited/tracked tags. Check out:
, built on the QT framework
, Uses the Chrome browser for its engine.