Does moving an app to Trash trigger its uninstaller?

Does moving an app to Trash trigger its uninstaller?

No!

Use an app like AppCleaner to remove an unwanted application you've installed, and its associated files/folders its created.

Here is an example using Adobe Acrobat Reader DC:

Had I just placed the Adobe Acrobat Reader DC.app in the Trash and emptied it, the other items listed would still remain.

^{Note: I'm not affiliated with the developer of the aforementioned application, just a satisfied user.}

Some management utilities will attempt to clean up for you, but there are no system-level processes that will.

One such is Hazel (https://www.noodlesoft.com/).