If you're being that restrictive you should consider creating a few simple form-based searches for that group of users and taking away their freestyle search interface entirely. That way this - I'm guessing newbie - group of users doesn't really need to learn SPL and stays within the boundaries set by the form developer. Unlike search term restrictions that cannot even contain a pipe the form-based approach puts no limits on your limits' complexity.
AFIK, you can't restrict an entire app in this way.
You can restrict a role by setting a search string, but I don't think it can be as complex as your search. But you could restrict a role to sourcetype=vxml for example. Then make the app available only to users that have that role.
That would get you partway there.