Yes, it is possible. The key is the Qt::WA_TranslucentBackground  attribute of QWidget
Here is a simple class that draws a round translucent window with a red background 50% alpha.
TranslucentRoundWindow.h:
#include <QWidget>
class TranslucentRoundWindow : public QWidget
{
    public:
        TranslucentRoundWindow(QWidget *parent = 0);
        virtual QSize sizeHint() const;
    protected:
        virtual void paintEvent(QPaintEvent *paintEvent);
};
TranslucentRoundWindow.cpp:
#include <QtGui>
#include "TranslucentRoundWindow.h"
TranslucentRoundWindow::TranslucentRoundWindow(QWidget *parent) : QWidget(parent, Qt::FramelessWindowHint)
{
    setAttribute(Qt::WA_TranslucentBackground);
}
QSize TranslucentRoundWindow::sizeHint() const
{
    return QSize(300, 300);
}
void TranslucentRoundWindow::paintEvent(QPaintEvent *)
{
    QPainter painter(this);
    painter.setRenderHint(QPainter::Antialiasing);
    painter.setPen(Qt::NoPen);
    painter.setBrush(QColor(255, 0, 0, 127));
    painter.drawEllipse(0, 0, width(), height());
}
If you want to be able to move this window with the mouse, you will have to override mousePressEvent, mouseMoveEvent and mouseReleaseEvent.