Sorry, not really. A screenreader is a separate, standalone application. In Windows, it utilises MSAA, an API provided by the operating system.
JS combined with Flash is the closest you will get: http://webaim.org/techniques/flash/media/detect.html Flash makes use of MSAA.
However, you'll get unreported users for users without Flash and users not on Windows. Screenreader users on mobile are growing rapidly http://webaim.org/projects/screenreadersurvey4/
The mac screen reader is called VoiceOver and is present on MacOSX and iOS.