My Qt app has today been accepted and is available on the App Store. So the answer is yes, Apple will accept Qt based applications.
Here's some information about my application. It written in C++ and uses Qt v4.7.2 under the LGPL license. The Qt frameworks are included in the app bundle (obviously, as LGPL requires I use dynamic linking instead of static). There are also some other frameworks, from Nikon and Canon, because its an app for remote control of DSLR cameras - see http:www.hartcw.com . These are only available compiled for Intel 32bit, hence this forces my app to also target 32bit, and so I have to use the 32bit Carbon build of Qt.
Regarding writing files to the local hard disk, it does not write anything to the bundle directory, but does write to this directory:
~/Application Support/Hart/Smart Shooter
It also writes Qt GUI state to this file (via the QSettings class)
~/Library/Perferences/com.hartcw.SmartShooter.plist
'Hart' is the company name as registered with Apple, and 'com.hartcw.SmartShooter' is the app identifier name, so I think this is what Apple checks against.
Also there were a couple of things I had to do regarding the plist file, see http://hartcw.com/francis/qt-and-the-mac-app-store
Infact it was accepted first time by Apple! It was in the 'waiting for review' stage for about 10 days, then transitioned to 'in review' for about 4 hours, and then went live on the app store.