Solution
No, in an Executable the LabVIEW Web Services are automatically enabled.
The LabVIEW Web Server can be programmatically enabled or disabled, but it would only take care of the Web Server meanwhile the Web Services are still enabled in the executable.
As soon as you start the executable, the Web Services starts with it (after all, this is the point at which a Web Service is deployed with an application). There is definitely no LabVIEW API that allows you to manually start/stop the Web Service.