What is the web connection for? Is it for user authentication? Is it for parsing data from a website? It really depends what you need an internet connection for, if you need some external data from a website or database then you would need to internally create some stores/sqlite db's to hold the data and sync that data when there is a connection.
If you are just running a client side app that you decided to create in HTML then I'd still use Sencha Touch, then Cordova to get it to compile natively.
You can always "Add to home screen" from Safari, to make it run locally. To do this, just visit the webpage when you have internet then add it to the homepage, it will run fullscreen without an internet connection; it will work fine offline IF AND ONLY IF you don't need to connect for any data.