Is it it illegal to want to work off the clock or legal? It is illegal for you to work off the clock without being paid. Since your employer is not only the one who has to pay you, but who is the one who will pay any fines if you are not paid for all the time you work, the employer gets to say what hours you work. You do not get to decide to work additional hours without your employer's approval.
Is is illegal to WANT to work off the clock? No. You can WANT to do anything you like. But it is illegal to work off the clock without being paid, and while not illegal, it is nonetheless a termination offense to work without authorization.
As well could I be terminated if I am working off the clock? Or just get a warining. Either could happen. Either would be legal. It will be up to the employer how much of a statement they want to make.
Two things I am tired of typing: 1.) A wrongful termination does not mean that you were fired for something you didn't do; it means that you were fired for a reason prohibited by law. 2.) The above answer, whatever it is, assumes that no legally binding contract or CBA expressly says otherwise. If it does, the terms of the contract apply.