So to clarify on this, I think that @everett was answering how to completely disable all success notifications in an app. Using CSS, like he was outlining you can completely hide that notice as a global setting.
As Justin is saying here, each query does have the option to hide it's success notification, or change the message to a custom option if the query is set to run when manually triggered. If the query is set to run when inputs change, that UI is hidden and the notification is disabled by default.

