I'm a little late to this thread seeing how it was started at the beginning of the year, but I have to disagree with the notion that it's the interpreter's job to just stand there and relay information, and anything else is outside of their job description.
The full job description of an interpreter is "communication and cultural mediator". In the case of a Deaf student not paying attention to the interpreter, it may not be realistic in that scenario to expect the hearing teacher to pick up on it. As long as the student is not being disruptive or obviously not paying attention (for instance, reading a comic book hidden underneath his text book) then the teacher may simply not be aware of the fact that he isn't paying attention. In her world, a student can still receive information even if not looking directly at the speaker, and it may simply not dawn on her that this is not the case in the world of sign language.
In this situation, I think it would be appropriate for an interpreter to act as a cultural mediator and say to the teacher, "I'm not sure if you realize this or not, but Billy is not paying attention to what I'm interpreting, and I'm not certain he is receiving the information being presented in the classroom." This could open up an opportunity to educate the teacher about Deaf culture, the interpreter's role, and to discuss strategies for encouraging the student to stay engaged in the classroom instruction.
Of course there is no one-size-fits-all solution to any dilemma an interpreter faces. Depending on the constellation of demands, what might be an effective control in one situation will not be in another. It's best not to think in terms of rigid boundaries.