I consider Qt to be more a framework than a library per se. The fact of being written in C++ is probably irrelevant, since you usually don't link to it from other projects (say ncurses, gtk based), you use it to build a Qt application or extend it (like the KDE project).
With boost you usually pick and choose and include parts of the (templated) libraries directly into your project directory, so you don't have to embrace it in full.
Sorry, but no. You can use libQtCore or libQtGui without the rest. Or just libQtCore + libQtSQL for a server. You can even mix them inside an application that is not a QApplication.
I think the Qt people might have something to say about that.