Is it possible for an AppleScript application's "Quit" button to override (i.e., cancel) an open dialog?
The short answer is, no.

The longer answer is: By design, an AppleScript's display dialog creates an application modal object, meaning that until the User responds to the controls of the object, the application waits until is receives appropriate input to that object in order for it to continue.

If a Cancel button exists and not the default button, it can be dismissed by pressing the Esc key or a Command-period key press to activate the Cancel button. If you use a Cancel button, you can trap the error and execute a return that will halt execution of the remaining code of the app.

If if doesn't have a Cancel button then it can't be dismissed without direct interaction or forced quit by any one of several methods.

To force quit:


You can option-right-click the app's Dock tile and select Force Quit from App's Dock tile context-menu.
Press Option-Command-Esc to bring up the Force Quit Applications dialog box.
Force quit it from Activity Monitor.
Its process can also be killed from Terminal in a few different ways, but beyond the scope of this answer as it's not a GUI method.


Also, ⌘Q doesn't work because it's grayed out in the App's Menu bar menu.

All this is also true within the Script Editor itself, not just with an AppleScript app. Once a display dialog is present it must be interacted with appropriately or the app forced quit by one method or another.