Can a WordPress site be converted into an iOS app? Maybe using something like PhoneGap to encapsulate the php?
I'm a developer at Clarity and we use PhoneGap to publish our native iOS application to the App Store.
From experience, wrapping our website in PhoneGap has been a really good way to get a native application that has native features like push notifications for "cheap".
The nature of Clarity itself requires you to be online to use the product: browse and search, request calls, ask questions, etc. For that reason, we never looked at providing offline support. If we can't find an internet connection, we show a very simple alert dialog.