You are asking about speech recognition, right? That's not supported by safari yet, maybe iOS 8 brings it.
Wrapping the web app using Phonegap might be a solution if you use one of the speech recognition plugins available, but your user will need to use the app instead the regular browser.
As you talk about Voice Over, thats for Text To Speech, not Speech recognition, Text To Speech is possible with iOS 7, take a look to this article http://www.sitepoint.com/talking-web-pages-and-the-speech-synthesis-api/ and this live demo http://aurelio.audero.it/demo/speech-synthesis-api-demo.html