Admin rights <-- all bets are off. :)
Why not enforce the app? By that I mean, EA to confirm the app is there. If it goes away, policy puts it back. They'll eventually give up.
You can lock the app using "chflags", which will prevent deletion unless you unlock it again. But if the students are able to get local admin rights, and they know what they're doing, it won't stop them. This would be more of a deterrent for those that don't know better.
sudo chflags uchg /Path/to/Application.app
You can try making the app immutable using chflags
but really just disable that account when not in use or don't give them the admin password is probably the best answer.
This does not stop an admin account from removing the immutable flag, it simply makes them learn how to use Unix. Which I am guessing a teenager, that has a ton of free time and access to Google will probably figure out
The user account in question was not an admin after all. I used the following command to lock the .app, when they try to delete it they get a request for admin privileges.
sudo chmod +a "<user> deny delete,delete_child,file_inherit,directory_inherit,chown,writesecurity" /Users/user>/Desktop/ApplicationLauncher.app