Can a WordPress site be converted into an iOS app? Maybe using something like PhoneGap to encapsulate the php?
That said... Things like Phonegap (web views) are a wonderful idea for utility apps because the performance is good enough for those (and hey even some games) and they end up being easily ported across many mobile operating systems.
I would look into Phonegap, Appgyver (a new and totally awesome one because parts of it will utilize the native OS and your app will feel more responsive), Appcelerator Titanium, and perhaps even the new Famo.us one. Also take a look at the Ionic Framework for some further ideas about mobile UI and what you can do with these web view style apps.