Here is an example of where exactly what you are asking has been done to good effect.
By inserting a line of code in your normal website, we detect which device you are on and redirect you to a HTML5 + Jqtouch version of the site which acts and looks a lot like a native app (especially on the iphone)
By inserting a line of code in your normal website, we detect which device you are on and redirect you to a HTML5 + Jqtouch version of the site which acts and looks a lot like a native app (especially on the iphone)
See http://www.pocketdiner.co.uk
We've had no problems so far so the answer to your question is yes - HTML5 is mature enough for mobile devices from our experience.