Opera and Google Earth are good examples of such apps - they suck. Both have non native and ugly user interface. So if you your app does more or less what other apps do, but looks like this, people will prefer the native cocoa apps.
Agreed, they have ugly Ui's but that's not Qt's fault. When you want an "Ok" button, a dialog or a check box in Qt, it's calling the EXACT SAME function that get's called when you do it without Qt. So by definition it is native. You should check it out. You might change your mind.