No, it doesn’t change. Hold down Option+Shift modifiers while click to the new Output sets the output of all selected tracks to the same (selected) output. If you hover over the output field, the tooltip should show you the Key Command.
My q-link Highlights on the mixer window, but in the project window it only changes the output of the one I’m clicking on, even if two are highlighted.
When I hold down Shift+Option the Q-Link is enabled in the MixConsole (even if the focus is in the Project window). If I search for the Q-Link in the KeyCommands, no KeyCommands is assigned on my side (default setup). So it seems it’s somehow hard-coded.