Should the mouse action which closes a dropdown menu trigger the actions under itself?

Assuming we have a dropdown menu which closes on a mouse click (instead of automatically when the mouse leaves the area).

Should this mouse click perform its standard actions, if the mouse happens to be above an element which can be clicked upon?

I've seen both versions being implemented in very similar applications.

If the rest of the user interface is complex, and can have context-sensitive items triggerable by mouse, it makes sense that the user has to click again to perform it. For example, in a web browser, it would be annoying if a link was followed because the user clicks only to close a dropdown menu. In a paint program, it's annoying when a new pixel is painted on the canvas because some menu was closed.

However, if there is an emergency stop button (or similar functionality) on the interface, it can be annoying if the user has to click twice if a menu was open somewhere.