Surely this is possible? I have been hunting through PyQt tutorials and documentation but cannot find the answer to it. Probably I just need to phrase my search query differently.
[Edit]
Thanks PEZ for the answer - more details including use of the .pyw
extension in Python Programming on Win32 chapter 20
I think you should be able to run your app with pythonw.exe.
An easy way to do this is to give your script a .pyw extension instead of the usual .py.
This has the same effect as PEZ's answer (runs the script using pythonw.exe).