Qt.WindowTransparentForInput flag with TapHandler/MouseArea

[necko1]

Is it possible to combine Qt.WindowTransparentForInput and TapHandler/MouseArea?

I want to make it so that the user can interact with something behind the window and also so that the window can see when the user has pressed the mouse button.
I know that Qt.WindowTransparentForInput literally disables this feature, but perhaps there is some other way around?

my code that I tried to implement:

import QtQuick
import QtQuick.Window

Window {
    visible: true

    width: Screen.desktopAvailableWidth
    height: Screen.desktopAvailableHeight
    flags: Qt.FramelessWindowHint | Qt.WindowStaysOnTopHint | Qt.Window | Qt.WindowTransparentForInput
    color: "transparent"

    Component.onCompleted: {
        showFullScreen()
    }

    TapHandler {
        onTapped: close()
    }
}

It will work if I remove the "Transparent for input" flag, but this way I won't be able to interact with anything behind the window. (for the first click)