Yes, it's possible to use QT with the above setup, the minor issues you're refering are most ones coming from the metacompiler system QT uses. There is some work in progress to support it well.
As a personal recommendation, I'll say give a look to the wxWidgets API, it's better than QT in my opinion, also with cross platform capabilities and good reputation, but more important, native widgets on each platform. Just compare how KDevelop (made in QT) and Code::Blocks (made in wxWidgets) looks in both Windows and Linux for example.
Also, if you plan to develop a plugin for C::B in the future, you'll need to use wxWidgets.
Having said that, I'd suggest you to try both APIs, and use the one you feel more comfortable.