Is the internal calendar or clock something an app is allowed to change?
No.

Source: This Stack Overflow answer.

Makes sense. Apple hardly allows apps to modify system-level stuff. It's easy to guess that the heavy sandboxing also means they cannot touch something as crucial as system time. Many things depend on the system time and even if Apple allowed apps to do that, it would take a lot of effort to make sure it worked without messing up other processes.