Graphics card that can't handle working to its full potential is already dead (as designed).

I didn't.
It was not required for my app to know about network adapters. Is that possible to do in cross-platform way using Qt -- I have no idea.

I concur. My Qt-powered multithreaded and networked (TCP&UDP) application is compiling and working nicely in linux, osx and win32 without any os-specifc #ifdefs.