Well, I seem not to be able to paint on it using such a test program:
#include <QApplication>
#include <QDesktopWidget>
#include <QPainter>
int main(int argc, char **argv){
dw->setAttribute(Qt::WA_PaintOutsidePaintEvent);
p.drawLine(0,0,dw->width(), dw->height());
return app.exec();
}
#include <QApplication>
#include <QDesktopWidget>
#include <QPainter>
int main(int argc, char **argv){
QApplication app(argc, argv);
QDesktopWidget *dw = app.desktop();
dw->setAttribute(Qt::WA_PaintOutsidePaintEvent);
QPainter p(dw);
p.drawLine(0,0,dw->width(), dw->height());
return app.exec();
}
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An alternative would be to catch a paintEvent for it, but I doubt it gets any paint events 
I managed to get a transparent top-level widget using the Qt::WA_PaintOnScreen attribute combined with other attributes but the drawback is that the background under the widget is not refreshed if it changes, so one would have to do that manually (somehow).
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